ludoM edoK

FKT.TAM 02 1- 10

YNU kinkeT satlukaF fitomotO kinkeT nakididneP nasuruJ

TIMIL SATIUYNITNOK NAD ISGNUF

)X( f = )X( f X

C

C

mil X = X X C

: nusuyneP

.T.M ,.dP.M ,ibutraM

)4 PS( naraggnagneP nad margorP nanusuyneP naanacnereP metsiS T nakididneP nasuruJ fitomotO kinke

002 5

2

RATNAGNEP ATAK

luduj nagned ludoM isgnuF haubeS satiuynitnoK nad timiL ini

kutnebmem kutnu hailuk nataigek malad naudnap iagabes nakanugid

utas halas bus - “ :utiay ,isnetepmok nad ,tafis ,pesnok nakanuggneM

la isalupinam ini ludoM .“isgnuf timil halasam nahacemep malad rabaj

I retsemes id akitametaM hailuk atresep aumes kutnu nakanugid tapad

iregeN satisrevinU kinkeT satlukaF fitomotO kinkeT idutS margorP adap

.atrakaygoY

miL rasad pesnok nakijasid ini ludom adaP satiuynitnoK nad ti

malad iapmujid kaynab gnay aynnahalasamrep nad isgnuF haubeS

.sitkarp nupuam sitiroet araces kiab ,kinket gnadib id aynnaparenep

sahabmem 1 rajaleb nataigeK .rajaleb nataigek agit sata iridret ini ludoM

.rabajlA isgnuF timiL :gnatnet K gnatnet sahabmem 2 rajaleb nataige : timiL

.irtemonogirT isgnuF K rajaleb nataige 3 gnatnet sahabmem : satiuynitnoK

.isgnuF haubeS

awsisaham hadum nagned ini ludom irajalepmem tapad kutnU

namahamep nad nauhategnep iaynupmem halet nakparahid gnatnet

pesnok - gnay rasad pesnok pesnok amaturet ini lah malad ,ayngnajnunem

gnatnet isgnuF rabajlA nad irtemonogirT isgnuF .

,atrakaygoY 5002 rebotkO

nusuyneP

.T.M ,.dP.M ,ibutraM

3

LUDOM ISI RATFAD

namalaH

AH LUPMAS NAMAL ............................................................................ 1 RATNAGNEP ATAK ............................................................................. 2

ISI RATFAD ................................................... ....................................... 3 YRASSOLG / NAHALITSIREP .... . ......................................................... 5

NAULUHADNEP . I ................................................................................. 6

ispirkseD .A ..... .... ........................................................................ . ....... 6

......................................................................................... taraysarP .B 6

.......................... ludoM naanuggneP kujnuteP .C ................................ 7

.......................................................... awsisaham igab kujnuteP .1 7

igab kujnuteP .2 nesod ...................................................... ............ 7

kA naujuT .D .................................................................................. rih 8

.................................................................................... isnetepmoK .E 8

....................................... naupmameK keC .F ..................................... 9

NARAJALEBMEP .II ...................................................................... . ....... 01

awsisahaM rajaleB anacneR .A ......................................................... 01

nataigeK .B ............................................................................. rajaleB 01

1 rajaleB nataigeK .1 ............. ........................................................ 01

...................... 1 rajaleb nataigek naujuT .a . ........ ...................... . 01

iretam naiarU .b ... ..................................................... . ................ . 01

........................................................................ 1 namukgnaR .c 1 .. 8

............................. 1 saguT .d ..................................................... . 02

......................................................................... 1 fitamrof seT .e . 02

bawaj icnuK .f set .. 1 fitamrof . ................................................... . 02

4

namalaH

2 rajaleB nataigeK .2 ........................................................... .......... 12

....................................................... 2 rajaleb nataigek naujuT .a 12

............................................ 2 iretam naiarU .b ........................... 12

......................................................................... 2 namukgnaR .c . 22

.................................................................................. 2 saguT .d . 32

fitamrof seT .e ... 2 ........... ........................................................... . 32

bawaj icnuK .f set fitamrof 2 ............... ...................................... .. 42

3 rajaleB nataigeK . 3 ........................................................... ......... 42

rajaleb nataigek naujuT .a 3 ....................................................... 42

iretam naiarU .b 3 ....................................................................... 42

namukgnaR .c 3 ..................................................... .................... 25

saguT .d 3 .................................................................................. 26

fitamrof seT .e ... 3 ...................................................................... 26

bawaj icnuK .f set fitamrof 3 ....... ........ ...................................... 27

ISAULAVE .III .............................................................................. ...... .. 28

.......................................................................... naaynatreP .A ....... . 28

............................................................................. nabawaJ icnuK .B 29

........................................................................ nasululeK airetirK .C 29

PUTUNEP .VI ................. ...................................................................... .. 03

AKATSUP RATFAD ............................................................................ . 13

5

/ NAHALITSIREP YRASSOLG

isgnuF ksiD uynitno nuf haubes halada : gnay isg kadit uata ulales kadit

upmem surenem suret isgnuf haubes uata kitit paites id agrah iayn

uata kitit adap agrah iaynupmem kadit imalagnem hanrep gnay

.utnetret lavretni

uynitnoK isgnuF surenem suret uata ulales gnay isgnuf haubes halada :

upmem yn kitit paites id agrah ia .

irtemonogirT isgnuF halada : aynagrah gnay isgnuf haubes halada

utnetret tudus utaus agrah helo nakutnetid .

isgnuF timiL halada : isgnuf haubes itakedid gnay satab ialin uata agrah

gnalib nagned itnagid uti isgnuf lebairav akij ialin itakednem gnay na

utnetret .

isinifedreT : utaus awhab nakataynem kutnu halitsi haubes halada

.utnetret agrah iaynupmem nagnalib

6

I BAB NAULUHADNEP

ispirkseD .A

ludoM luduj nagned isgnuF satiuynitnoK nad timiL ini

sahabmem rasad pesnok gnatnet atres isgnuF satiuynitnoK nad timiL

aynnahalasamrep gnay id aynnaparenep malad iapmujid kaynab

.sitkarp nupuam sitiroet araces kiab ,kinket gnadib gnay iretaM

,rabajlA isgnuF timiL : pukacnem irajalepid irtemonogirT isgnuF timiL

d .isgnuF haubeS satiuynitnoK na

.rajaleb nataigek aud sata iridret ini ludoM 1 rajaleb nataigeK

:gnatnet sahabmem ,rabajlA isgnuF timiL 2 rajaleb nataigeK

:gnatnet sahabmem irtemonogirT isgnuF timiL rajaleb nataigeK . 3

:gnatnet sahabmem ynitnoK .isgnuF haubeS satiu paites adaP

nad laos hotnoc nagned ipakgnelid ulales rajaleb nataigek

nahital atreseb aynnasahabmep - utnabmem kutnu aynulrepes nahital

.nakparahid gnay isnetepmok iapacnem malad awsisaham

ludom irajalepmem iaseles haleteS nahurulesek araces ini

nakparahid awsisaham isnetepmok bus iaynupmem “ nakanuggneM

timil halasam nahacemep malad rabajla isalupinam nad ,tafis ,pesnok

“isgnuf

taraysarP .B

iretam isireb ini ludoM - iretam nagnukud nakulremem gnay iretam

ial gnay n iretam nupadA .aynmulebes irajalepid halet aynitsemes -

let aynsurahes gnay rasad iretam hailuk atresep helo imahafid ha id

pesnok halada amaturet fitomotO kinkeT nakididneP nasuruJ rasad

.irtemonogirT isgnuF nad rabajlA isgnuF : gnatnet

7

kujnuteP .C ludoM naanuggneP

awsisahaM igab kujnuteP .1

malad akam ,lamiskam gnay rajaleb lisah helorepid ragA

ulrep gnay rudesorp aparebeb ada ini ludom nakanuggnem

: nial aratna nakanaskalid nad ,nakitahrepid

amaskes nagned imahaf nad halacaB .a pesnok naiaru - pesnok

alup imahaf naidumek ,ini ludom adap nakijasid gnay sitiroet

pesnok naparenep - hotnoc malad tubesret pesnok - laos hotnoc

iretam ada hisam askapret aliB .aynnaiaseleynep arac atreseb

d imahafid asib muleb nad salej gnaruk gnay ne iab nag arap k

upmagnem gnay nesod adapek nakaynanem tapad awsisaham

.nahailukrep nataigek

,iridnam araces )nahital laos( fitamrof sagut paites nakajrek aboC .b

raseb aparebes iuhategnem kutnu nakduskamid ini lah

ret awsisaham paites ikilimid halet gnay namahamep padah

iretam - .rajaleb nataigek paites adap sahabid gnay iretam

iretam iasaugnem muleb awsisaham aynnaataynek malad alibapA .c

nad acabmem igal ignalu aboc ,nakparahid gnay level adap

nahital igal nakajregnem - halaynatreb ulrep ualak nad aynnahital

od adapek gnay nahailukrep nataigek upmagnem gnay nes

nakulremem natukgnasreb gnay iretam ualaK .natukgnasreb

taraysarp awhab naknikay akam )taraysarp( lawa namahamep

raneb duskamid gnay - .ihunepid hadus raneb

nesoD igaB kujnuteP .2

nataigek paites malaD nad sagut iaynupmem nesod ,nahailukrep

: kutnu narep

a. .rajaleb sesorp nakanacnerem malad awsisaham utnabmeM

b. sagut iulalem awsisaham gnibmibmeM - nahital uata sagut - nahital

.rajaleb bahat malad naksalejid gnay

8

c. ad urab pesnok imahamem malad awsisaham utnabmeM n

.nakulrepid alibapa awsisaham naaynatrep bawajnem

d. gnay nial rajaleb rebmus seskagnem kutnu awsisaham utnabmeM

.nakulrepid

e. .nakulrepid akij kopmolek rajaleb nataigek risinagrogneM

f. .nakulrepid akij gnipmadnep nesod/ilha gnaroes nakanacnereM

g. lave nakadagneM isnetepmok naiapacnep padahret isau

.nakutnetid halet gnay awsisaham naanaskalep tubesret isaulavE -

.rajaleb nataigek rihka paites adap ayn

rihkA naujuT .D

ludom malad rajaleb nataigek iretam hurules irajalepmem haleteS

parahid awsisaham ini nak tapad : “ nad ,tafis ,pesnok nakanuggneM

“isgnuf timil halasam nahacemep malad rabajla isalupinam .

isnetepmoK .E

ludoM FKT 02 1- luduj nagned 10 satiuynitnoK nad timiLisgnuF haubeS kutnebmem akgnar malad nususid ini bus -

isnetepmok “M rabajla isalupinam nad ,tafis ,pesnok nakanuggne

“isgnuf timil halasam nahacemep malad .

iapacnem kutnU bus - surah uluhad hibelret ,tubesret isnetepmok

bus iapacid tapad - aynajrek kujnu airetirk atreseb isnetepmok bus

am nagned rajaleb pukgnil iulalem iagabes narajalebmep kokop iret

tukireb :

9

F . naupmameK keC

jalepmem mulebeS ira ludoM 102 FKT – adnat nagned halisi ,ini 10

( kec ikilimid halet gnay isnetepmok nakkujnunem gnay naaynatrep )

: nakbawajgnuggnatrepid tapad nad rujuj nagned awsisaham

buS

isnetepmoK naaynatreP

nabawaJ “aY“ nabawaJ aliB nakajreK aY kadiT

anuggneM -

,pesnok nak nad ,tafis

isalupinam rabajla

malad nahacemep

halasam nad timilstiuynitnok

isgnuf .

,naitregnep :naksalejnem upmam ayaS .1

tafis nad ,isaton - .isgnuf timil tafis

1 fitamroF seT

1 romoN

asamrep nakiaseleynem tapad ayaS .2 - .rabajla isgnuf timil nahal

1 fitamroF seT

2 romoN asamrep nakiaseleynem tapad ayaS .3 -

.irtemonogirt isgnuf timil nahal

2 fitamroF seT

asamrep nakiaseleynem tapad ayaS .4 - isgnuf haubes satiuynitnok nahal

3 fitamroF seT

bawajnem awsisaham alibapA kadiT ini ludom irajalep akam

bawajid gnay iretam iauses kadiT .tubesret

buSisnetepmoK

airetirK ajreK kujnU

pukgniLrajaleB

narajalebmeP kokoP iretaM

pakiS nauhategneP nalipmarteK

anuggneM - ,pesnok nak

,tafis nad isalupinam

rabajla malad

nahacemep halasam

timil nadtiuynitnok s

isgnuf .

naksalejneM .1

naitregnep , isaton nad

tafis - il tafis tim. isgnuf

2 iaseleyneM . -mrep nak asa -

timil nahal isgnuf a rabajl

3 iaseleyneM . -asamrep nak -

timil nahal isgnuf

irtemonogirt .5 naksalejneM .4

satiuynitnok haubes

isgnuf

aitregneP .1 n ,

isaton nadtafis - tafis timil

. isgnuf

2 . L isgnuf timi a rabajl .

3 . L isgnuf timi irtemonogirT

4 . satiuynitnoK haubes

isgnuf

nad itileT

tamrec malad

silunem lobmis

alem nad -rep nakuk -

nagnutih

naitregneP .1 ,

isaton nad ,tafis - tafis timil

. isgnuf 2 . L isgnuf timi

a rabajl .

3 . L isgnuf timi irtemonogirT

4 . satiuynitnoK haubes

isgnuf

gnutihgneM

nagned rudesorp lisah nad

raneb gnay

01

II BAB NARAJALEBMEP

awsisahaM rajaleB anacneR .A hawab id lebat isignem nagned rajaleb nataigek anacner haltauB

.iaseles haletes nesod adapek rajaleb itkub halatnim nad ini

nataigeK sineJ laggnaT utkaW tapmeTrajaleB

nasalAnahabureP

faraPnesoD

nad isaton ,naitregneP .1 tafis - isgnuf timil tafis

rabajla isgnuf timiL .2

nogirt isgnuf timiL .3 .irtemo haubes satiuynitnoK .4

isgnuf

.rajaleB nataigeK .B

: 1 rajaleB nataigeK .1 rabajlA isgnuF timiL

: 1 rajaleB nataigeK naujuT .a 1 .) tafis nad isaton ,naitregnep naksalejnem tapad awsisahaM -

.isgnuf timil tafis

2 .) aM m tapad awsisah ne iaseley ep nak isgnuf timil nahalasamr

.rabajla

: 1 iretaM naiarU .b tafiS nad isatoN ,naitregneP .)1 - tafis isgnuF timiL .

kutnU isgnuf timil gnatnet naitregnep imahamem tapad

gnuf haub aud irad ialin nakitahrep akam akij tukireb X is

gnisam - isgnuf halada amatrep isgnuF .aynagrah iracid gnisam

isgnuf halada audek isgnuf gnades ,surul gnidnabreb gnay

.kilabret gnidnabreb gnay

11

: aynlasim ,surul gnidnabreb isgnuf kutnU .)a X

f = )X( nagned ( X ) ilsa nagnalib = 4

X 004 001 2 1 40,0 400,0 4000,0 .......

)X( f 001 52 5,0 52,0 10,0 100,0 1000,0 .......

iraD rah irebid X akij awhab salej kapmat sata id ratfad ag

aggnihes ,licek nikam aguj )X( f agrah akam licek nikam

“ gnay X kutnu ilakes licek tama tagnas nakatakid ( ”

“ naka aguj )X( f agrah akam ) lon itakednem tama tagnasilakes licek araces silutid ini naataynreP .) lon itakednem ( ”

: isaton nagned sitametam

X X 0 = timil takgnisid gnires uata 0 = mil X 4 0 X 4 0

ayntujnaleS ,awhab nakitkubid tapad aguj akij nikam X

X kutnU .alup raseb nikames naka )X( f agrah akam raseb

kat itakednem nakatakid ( ”ilakes raseb tama tagnas“ gnay

ama tagnas“ naka aguj ) X( f agrah akam ) aggnihret t

araces silutid ini naataynreP .)aggnihret kat( ”ilakes raseb

: isaton nagned sitametam

X X

= timil takgnisid gnires uata mil = X 4 X 4

kutnu awhab mumu araces naklupmisid tapad aynrihkA

: ukalreb tapad surul gnidnabreb isgnuf aumes

= )X( f timil 0 nad = )X( f timil X 0 X

21

b gnidnabreb isgnuf kutnU .) kilabret : aynlasim ,

4 = )X( f gned ( na X ) ilsa nagnalib =

X

X 1 2 8 04 004 000.4 000.04 ....... )X( f 4 2 5,0 1,0 10,0 100,0 1000,0 .......

iraD agrah irebid X akij awhab salej kapmat sata id ratfad

akam raseb nikam kutnu aggnihes ,licek nikam )X( f agrah

“ gnay X ilakes raseb tama tagnas itakednem nakatakid ( ”

“ naka )X( f agrah akam ) aggnihret kat licek tama tagnasilakes araces silutid ini naataynreP .) lon itakednem ( ”

: isaton nagned sitametam

4 4 0 = timil takgnisid gnires uata 0 = mil X X X X

ayntujnaleS ,awhab nakitkubid tapad aguj akij nikam X

gnay X kutnU .raseb nikames naka )X( f agrah akam licek

“ ilakes licek tama tagnas ) lon itakednem nakatakid ( ”

“ naka )X( f agrah akam ilakes raseb tama tagnas kat( ”

ynreP .)aggnihret nagned sitametam araces silutid ini naata

: isaton

4 4

= timil takgnisid gnires uata = mil X 0 X X X 0

kutnu awhab mumu araces naklupmisid tapad aynrihkA

: ukalreb tapad kilabret gnidnabreb isgnuf aumes

0 = )X( f timil nad = )X( f timil X X 0

31

iraD naitregnep haubes libmaid tapad tubesret naiaru

: awhab isgnuF timiL gnay satab agrah haubes halada

airav akij tubesret isgnuf helo itakedid utaus itnagid aynleb

aynsalej hibel kutnU .utnetret agrah itakednem gnay agrah

: tukireb hotnoc nakitahrep

( timil X = ) 4 + 6 = 4 + 2 X 2

adaP akgna tubesret hotnoc 6 halada timil uata agrah

satab gnay akgna itnagid X akij ) 4 + X ( isgnuf irad

aynlasim ,2 itakednem 100,2 naklisahgnem gnay 100,6

uata 9999,1 naklisahgnem gnay 9999,5 uti agrah audek

akgna itakednem ataynret 6 akgna idaJ . 6 agrah halnakub

gnay akgna ( satab agrah aynah ipatet ,kaske .) itakedid

isgnuf timil agrah akam amas gnay naralanep nagneD

kutneb nagned - : aynlasim ,nakutnetid tapad aynnial kutneb

X2 ( timil .)1( 2 X4 + – 2 = ) 3 . 12 4 + . 1 – 3 = 3 X 1

timil .)2( X3 ( 2 3 = ) 5 + X4 + . 2 4 + . = 5 + + = 5 + X

6 X6 . 21 2 = = = timil .)3(

X 2 X 2 2 – 0 2

X 6 6 0 6 0 = = = timil .)4(

X 5 X5 6 . 03 6

2 2 2 0 = = = timil .)5(

X .5 4 + X5 4 +

2 2 3 + X . 3 + 3 + = = = = timil .)6(

X 5 5 5 5

41

tafiS – isgnuF timiL tafis :

lisah padahret narusulenep iraD - timil nagnutihrep lisah

tafis iaynupmem isgnuf timil awhab naktubesid tapad isgnuf -

: tukireb iagabes tafis

k = k timil .)1( X C

C = X timil .)2(

X C

timil .)3( )X( f timil .k = )X( f . k

X X C C

)X( f [ timil .)4( + )X( f timil = ] )X( g + )X( g timil

X X C X C C

)X( f [ timil .)5( . mil = ] )X( g )X( f ti . )X( g timil

X X C X C C

)X( f [ timil .)6( : )X( f timil = ] )X( g : )X( g timil

X X C X C C

] )X( f [ timil .)7( n = ] )X( f timil [ n X X C C

timil .)8( = ] )X( f )X( f timil X X C C

natataC 0 = )X( g timil agrah lasa 6 romon tafis kutnU : X C

)X( f timil : 8 romon tafis kutnU > 0

X C

51

rabajlA isgnuF timiL .)2

halet anamiagabes isgnuf timil pisnirp nakrasadreB

iaruid akam rabajla isgnuf halada )X( f akij ,sata id nak

: tukireb iagabes namodep nagned gnutihid tapad aynagrah

) liir nad natsnok nagnalib halada k nad C (

k = )C( f alibapa k = )X( f timil .)a X C

k = )X( f timil .)b = )C( f alibapa

X 0 C

0 alibapa 0 = )X( f timil .)c = )C( f

X k C

k ( f alibapa 0 = )X( f timil .)d = )

X

= )X( f timil .)e isinifedret kadit uata utnetret kadit alibapa X C

0 ( uata ; : halada )c( f agrah – )

0

apureb isgnuf haubes timil nagnutihrep lisah ataynret akiJ

kutneb aratna id utas halas - kutneb isinifedret kadit sata id

kutneb ( e ) burep nakukalid surah akam naajregnep arac naha ,

uata ulud aynlaos kutneb nakanahredeynem nagned aynlasim

arates gnay nial kutneb nagned laos kutneb nakataynem

aggnihes .) isinifedret ( utnetret kutneb malad lisah helorepid

os kutneb naanahredeynep arac nupadA aynlasim tubesret la

nawakes kutneb nagned nakilagnem ,nakrotkafmem nagned

61

nad ,aguj nawakes kutneb nagned aynigabmem naidumek

bes a .aynlaos kutneb gnutnagret ayniag

laoS hotnoC :

gnutiH hal isgnuf timil - isgnuf ini tukireb !

.)a l ( timi X5 2 – 3X ) 4 + ( timil .)e X5 2 – ) X4 X X 2

X X3 2 + 3 + X2

b .) l timi f .) l timi X X 5 – X 5 4X2 + 3 X – 2

X2 – 3 + X4 X2 – 9 + X6

c .) l timi g .) l timi X X3 1 2 X + – X 2 X 3 2 X + – 21

4 3X + 5

d .) l timi h .) l timi X X 5 + X 3 X – 2

bawaJ :

.)a l ( timi X5 2 – X3 4 + ) = 2.5 2 – 3 2. 4 + = 81 X 2

5.3 X3 51

)b . l timi = = = X X 5 – 5 5 – 5 0

X2 – 3 + X4 12 – 4. 3 + 1 0

c .) l timi = = = 0 X X3 1 2 X + – 3 2 .12 1 + – 2 2

4 4 4

d .) l timi = = = 0 X 5 + X 5 +

( timil .)e X5 2 – ( = ) X4 5. 2 – .4 = ) –

X

71

habuid surah akam ,isinifedret kadit kutneb aynlisah anerak

: tukireb iagabes arac nagned

( X5 2 + X4 ) ( timil X5 2 – ) X4 = ( timil X5 2 – ) X4 . X X ( X5 2 + X4 )

( X5 2 – X4 ).( X5 2 + X4 ) X5 2 – X4 timil = = timil

X ( X5 2 + X4 ) X X5 2 + X4

ualak hisam ini kutneb adap nakisutitsbusid X agrah

inifedret kat kutneb tapadid aumes aynmulebes akam ,igal is

X :utiay ( iggnitret takgnap X igabid ukus 2 uata X 4 )

X5 2 / X2 – X4 / X2

= : idajnem timil X ( X5 2 / X 4 + X4 / X4 )

5 – 4 / X 5 – /4 = timil =

X 5 / X2 + 4 / X3 5 / 2 + 4 / 3

5 – 0 5 = = =

0 + 0 0

X2 3 + X2 + 2 2 + . 3 + f .) l timi )isinifedret kat( = =

X 4X2 + 3 X – 2 4. 2 3 + . – 2

habuid surah akam ,isinifedret kadit kutneb aynlisah anerak

utiay X nagned ukus aumes igabmem arac nagned 2.

X2 3 + X2 + X2 / X2 2 + X/ X2 X/3 + 2 l timi timil =

X 4X2 + 3 X – 2 X 4X2 / X2+ 3 /X X2 – /2 X2

1 2 + / X/3 + X 2 1 2 + / /3 + 2 1 0 + 0 +

= = timil =

81

X 4 + 3/ X – /2 X2 4 + 3/ – /2 2 4 0 + – 0

= ¼

X2 – 3 9 + X6 2 – 6. 0 9 + 3 g .) l timi ) isinifedret kat ( = =

X X 3 2 X + – 3 21 2 3 + – 0 21

: aynnakrotkafmem arac nagned utiay ,habuid surah akam

X2 – X( 9 + X6 – X( ) 3 – X )3 – 3 l timi timil = timil = X X 3 2 X + – X 21 X( 3 X( )4 + – X )3 X 3 4 +

3 – 0 3 = timil = ---- = 0

X 3 3 7 4 +

3X + 3 5 X /3X + 3/5 X + 1 3/5 X h .) l timi = l timi timil =

X 3 X – X 2 3X 3/ X – 3/2 X X 1 – 3/2 X

0 + 1

= = 1 1 – 0

.c namukgnaR : 1 tregneP .)1 tafiS nad isatoN ,nai - isgnuF timiL tafis .

.)a isgnuF timiL helo itakedid gnay satab agrah haubes halada

gnay agrah utaus itnagid aynlebairav akij tubesret isgnuf

.utnetret agrah itakednem

.)b isgnuf timiL X kutnu X itakednem C on nagned silutid isat :

)C( f = )X( f timil X C

tafiS .)c - : isgnuf timil tafis nagned ( , k C R lae )

k = k timil .)1( X C

C = X timil .)2(

91

X C

imil .)3( )X( f timil .k = )X( f . k t X X C C

)X( f [ timil .)4( + )X( f timil = ] )X( g + )X( g timil X X C X C C

)X( f [ timil .)5( . timil = ] )X( g )X( f . )X( g timil X X C X C C

)X( f [ timil .)6( : )X( f timil = ] )X( g : )X( g timil X X C X C C

] )X( f [ timil .)7( n = ] )X( f timil [ n X X C C

timil .)8( = ] )X( f )X( f timil X X C C

natataC 0 = )X( g timil agrah lasa )6( romon tafis kutnU : X C

)X( f timil : )8( romon tafis kutnU > 0 X C

rabajlA isgnuF timiL .)2

akiJ halada )X( f timil agrah akam ,rabajla isgnuf haubes

: tukireb iagabes namodep nagned iracid tapad )X( f irad

k = )C( f alibapa k = )X( f timil .)a

X C k

= )X( f timil .)b = )C( f alibapa X 0 C

0

= )C( f alibapa 0 = )X( f timil .)c X k C

k

( f alibapa 0 = )X( f timil .)d = ) X

02

= )X( f timil .)e isinifedret kadit uata utnetret kadit alibapaX C

0 ( uata ; : halada )C( f agrah – )

0 .d 1 saguT :

isgnuf timil halgnutiH - : ini tukireb isgnuf

X2 – 4 X4 – 3X2 – X2 timil .)2 timil .)7 -

X 2 X2 – 3X 2 + X 0 X2 5 – 52 – X 2 1+X 3 +

timil .)3 timil .)8 - X 0 X X 2X – 1

( timil .)4 X2 3 + X – X2 – X 3( timil .)9 ) X – 4 – 9X2 – )3 X X

.e fitamrof seT : 1 .)1 tafis nad isaton ,naitregnep : halnaksaleJ - ! isgnuf timil tafis

.)2 isgnuf timil halgnutiH - ! tukireb isgnuf

X2 + 2X – 51 3 4 a .) timil d ( timil .) – ) X 5 X2 – 25 X 2 X2 – 4 X – 2 X2 – 4 3 + X X3 – 3X2 – X 4 + b timil .) e timil .) -

X 3 X2 – X – 6 X X2 2 + 3X3 – 7 3 – 9 – X2 5X 1+ + 7 c timil .) f timil .) -

X 0 X5 X 5X – 02

.f fitamroF seT bawaJ icnuK : 1 .)1 isgnuF timiL itakedid gnay satab agrah haubes halada helo

gnay nagnalib utaus itnagid aynlebairav akij tubesret isgnuf .utnetret agrah itakednem isgnuf timiL X kutnu X itakednem C

isaton nagned silutid )C( f = )X( f timil : X C

12

isgnuf timiL tafis iaynupmem - afis tafis itrepes t - isarepo tafis.natsnok nagnalib rabajlaa/kitamtira

.)2 a .) .)c 51/1 e .) 3/1

b .) 5/2 d .) .)f 5

2 . rajaleB nataigeK 2 : gnuF timiL irtemonogirT is

rajaleB nataigeK naujuT .a 2 : isgnuf timil nahalasamrep nakiaseleynem tapad awsisahaM

.irtemonogirt

iretaM naiarU .b 2 :

irtemonogirT isgnuF timiL

il rasad edi nagneD isgnuF timil nagned amas gnay tim

malad id akam ,aynmulebes nakiaruid anamiagabes rabajlA

sumur tapadid irtemonogirT - : tukireb iagabes rasad sumur

X nis X timil . 1 = 1 uata timil = 1

X X X 0 X nis 0

X gt X timil . 2 = 1 uata timil = 1

X X 0 X X gt 0

tukireb iagabes idajnem saulrep id tapad tubesret sumur audeK :

Xa nis Xa timil . 3 1 = uata timil 1 =

X X Xa 0 Xa nis 0

Xa Xa gt timil . 4 1 = uata timil 1 =

X X Xa 0 Xa gt 0

nis n Xa a n X n

22

timil . 5 1 = ata u timil 1 = X a 0 n X n X nis 0 n Xa

gt n a Xa n X n timil . 6 1 = uata timil 1 =

X a 0 n X n X gt 0 n Xa

hotnoC isgnuf timil nakutneT : – : ini hawab id isgnuf

X3 nis gt X6 timil .1 ---------- timil .3 ----------

X X X 0 X7 nis 0 X gt s ni 2 3X

timil .2 --------- timil .4 -- -------- X X X5 0 0 7X2

bawaJ :

3 X3 nis X3 nis

.1 timil timil = . = 1. = 3 3 X X X 0 1 X3 0

4 4 X4 gt X4 gt 4

timil .2 timil = 1 = . = - X 0 X X5 X4 0 5 5 5

gt X7 X6 gt 6X 6 6 6

timil .3 = timil = 1 1 = - X X X7 nis 0 7 X6 X7 nis 0 7 7

s ni 2 3 X nis 2 3 X 9

timil .4 timil = . - X 0 7X2 X 0 9X2 7

9 9

. 1 = = - 7 7

.c namukgnaR 2 :

apad raseb sirag araces irtemonogirT isgnuF timiL nakadebid t

nem aj : mumu sumur aud id ) liir nagnalib halada n nad a akij (

nis n Xa a n X n 1 timil . 1 = uata timil 1 =

32

X a 0 n X n X nis 0 n Xa

gt n a Xa n X n 2 timil . 1 = uata timil 1 =

X a 0 n X n X gt 0 n Xa

.d 2 saguT : isgnuf timil halgnutiH – isgnuf irtemonogirT : ini tukireb

X2 soc + 1 X gt timil .1 --------- timil .6 ---------------

X X X3 nis 0 X soc 0

X nis X5 gt – X soc timil .2 ------- timil .7 ------------------

X X X3 0 1 0 – X2 nis

nis 2 gt + X 2 1 X – X2 soc timil .3 -------------------- timil .8 ---------------

X 0 2/1 X 2 X X 0 2

1 – X soc X( timil .9 – X( gtoc .) 5 – 5 )

timil .4 ------------- X 5 X X 0 2

X3 nis . X nis X nis . X

timil .5 ----------------- timil .01 -----------------

X 1 0 – X4 soc X 1 0 – X4 soc

.e fitamrof seT 2 : isgnuf timil halgnutiH – isgnuf irtemonogirT ini tukireb

nis 3 X 1) timil . --------- )4 . X( timil – )2 esoc X( c – )2

X 0 gt 8 X X 2

tg3 2 X . X3 nis 4 nis X 2) timil . ------- )5 timil . -- ----------------

X 0 5X3 X 0 1 – soc 01 X

nis 2 3 gt + X 2 4 1 X – soc 7 X 3) timil . -------- ------------ )6 timil . ------ ---------

X 0 5 X 2 X 0 4 X 2

42

fitamroF seT bawaJ icnuK .f : 2

.)1 8/3 .)4 1

)2 . 5/8 .)5 52/6

.)3 5 .)6 6 8/1

3 . rajaleB nataigeK 3 : isgnuF haubeS satiuynitnoK

rajaleB nataigeK naujuT .a 3 : awsisahaM ad nem tap p nakiaseley nahalasamre satiuynitnok

.isgnuf haubes

iretaM naiarU .b 3 :

isgnuF haubeS satiuynitnoK

alibapa C = X kitit id uynitnok nakatakid )X( f isgnuf haubeS

tarays ihunemem - : ini hawab id tarays

.a ifedret )C( f .ada )C( f agrah aynitra ,isin

.b ada aguj ) X ( f timil X C

.c ) C ( f = ) X ( f timil

X C

kadit sata id tarays agitek irad hibel uata utas halas ualaK

d gnay isgnuf akam ,ihunepid isgnuf iagabes nakatakid naikime

gnay .C = X id )uynitnok kadit( uynitnoksid gnay isgnuf ayntujnaleS

.uynitnok isgnuf iagabes tubesid kitit paites id uynitnok

hotnoC :

.a X = )X( f isgnuF 2 paites kutnu babes ,kitit paites id uynitnok 3 +

tarays ihunepid ulales C = X - isgnuf haubes nauynitnokek tarays .

X 2 .b = )X( f isgnuF ------- sid )2( f babes ,2 = X kitit id uynitnok = ---

X – 2 0

isinifedret kadit )2( f aggnihes .

52

X 2 + 2 6 .c = )X( f isgnuF -------- = ) 2 ( f babes ,2 = X id uynitnoksid -

X – 2 0

X kutnu )X( f timil nupiksem utnetret kadit itrareb gnay .ada 2

satiuynitnok nataraysrep nakitahrepmem nagned ayntujnaleS

lavretni nakutnetid aguj tapad ,isgnuf utaus - anam id lavretni

nok kadit isgnuf haubes .uynit

hotnoC : isgnuf hakanam lavretni adaP - isgnuf tukireb sid .uynitnok

4 .)1 = )X( f X - 2 .)2 = )X( f --------------

²X - 9

bawaJ : 1) = )X( f . X - 2

)X( f alib uynitnok kadit gnay isgnuf idajnem naka )X( f

hawab id akij idajret utiay ,)layahk( aynagrah ada kadit

fitagen agrahreb raka , X : aggnihes - 0 < 2 2 < X

)X( f idaJ sid : lavretni adap uynitnok X { | } 2 < X

4 2) . = )X( f -------------

²X - 9

²X akij uynitnoksid naka ini isgnuF - 9 ≤ 0

²X - 9 ≤ 0

X ( - ) 3 . ) 3 +X ( ≤ 0

- 3 ≤ X ≤ 3

)X( f idaJ sid : lavretni adap uynitnok

X { - 3 ≤ X ≤ } 3

.c namukgnaR 3 :

C = X kitit id uynitnok nakatakid )X( f isgnuf haubeS

tarays ihunemem alibapa - : ini hawab id tarays

62

.a .ada )C( f agrah aynitra ,isinifedret )C( f

.b ada aguj ) X ( f timil X 0

.c ) C ( f = ) X ( f timil

X 0

k irad hibel uata utas halas ualaK kadit sata id tarays agite

isgnuf iagabes nakatakid naikimed gnay isgnuf akam ,ihunepid

isgnuf ayntujnaleS .C = X id )uynitnok kadit( uynitnoksid gnay

uynitnok isgnuf iagabes tubesid kitit paites id uynitnok gnay : 3 saguT .d

.)1 isgnuf hakanaM - isgnuf nakapurem gnay ini tukireb isgnuf

uynitnok aynitkub nakkujnut nad ,kitit paites id .?

.a 2 + X = ) X ( f

X2 4 + = ) X ( f .b ------ -----

X – 2

X 2 X2 + + 8 = ) X ( f .c ------ ------------

4 + X

.)2 isgnuf hakanam lavretni uata kitit adaP - kadit ini tukireb isgnuf ? uynitnok

X X3 + 72

= ) X ( f .)a -------- = ) X ( f .c - -------- X – X 2 – 3

X5 – X 1 2 – 52 = ) X( f .)b ----------- = ) X ( f .d - -- -----------

X3 – X 2 2 – X3 – 01

.e fitamrof seT 3 : .)1 halnakataK gnuf is - uynitnok ini tukireb isgnuf kadit uata nad ,

.? aynitkub nakkujnut

72

.)a = ) X ( f 3 X – = )X( f .)d 4 X2 + X6 – 7

X2 + 9 X4 b) = ) X ( f . ------ ---- - .)e = )X( f - -

X – 3 X – 2

c) = ) X ( f . X4 2 6 +

.)2 isgnuf hakanam lavretni uata kitit adaP - kadit ini tukireb isgnuf ? uynitnok

5 X X3 + 1

= ) X ( f .)a -------- = ) X ( f .c - -------- X + 4 X – 1

2 X – 3 X2 + 2 1 + X = ) X( f .)b ----------- = ) X ( f .d - -- -----------

X + 6 X 2 – 4

.f fitamroF seT bawaJ icnuK 3 :

.)a .)1 agitek ihunepid ulales babes ,C = X kitit paites id uynitnoK

isgnuf satiuynitnok nataraysrep

.)b = X id uynitnok kadiT t )3( f babes 3 .isinifedret kadi

.)c X4 lavretni adap uynitnok kadiT 2 6 < < X uata 5,1

< X aumes kutnu babes isinifedret kadit )X( f 5,1

agitek ihunepid ulales babes ,C = X kitit paites id uynitnoK .)d

uynitnok nataraysrep isgnuf sati

X id uynitnok kadiT .)e ≤ ( f babes 2 ≤ .isinifedret kadit )2

2 .)a .) kitit adaP X = – 4

b .) : lavretni adaP X { X ≤ – 6 }

c .) kitit adaP X = 1

d .) kitit adaP X = 2 nad X = – 2

82

III BAB ISAULAVE

naaynatreP .A

.1 isgnuf timil halgnutiH - ! tukireb isgnuf ) 04 = eroks (

X2 + 4 X – 5 X5 3 + X2 2 – X3 1 + a timil . c timil . -

X 1 X2 – 1 X X3 3 + X4 2 – 5 4 – 61 + X5 3X –1 + 4 b timil . d timil . -

X 0 7X X 3X – 5

2 . isgnuf timil halgnutiH – isgnuf irtemonogirT ini tukireb ) 04 = eroks ( !

nis 4 2 X . X nis 3 nis X a timil . ------- c timil . -- ----------------

X 0 3X4 X 0 1 – soc 8X

nis 3 2 gt + X 3 X 1 – soc 5 X b timil . -------- ------------ d timil . ---------------

X 0 6 X 3 X 0 2 X 2

3 . halnakataK isgnuf - uynitnok ini tukireb isgnuf kadit uata nad , akij

) 02 = eroks ( ? aynkatel anam lavretni uata kitit adap ,kadit

.a = ) X ( f 2 X + X2 = )X( f .c 5 2 X5 + – 4

X2 + 61 X3 = ) X ( f .b ------ ---- - d . = )X( f - -

X – 4 X – 7

92

nabawaJ icnuK .B .1 .a 3 .c 1 ⅔

.b – 65/5 .d 1 3/

.2 .a 5 3/1 .c 23/3

.b ½ 1 .d ¼ 6

.3 C = X kitit paites id uynitnoK .a

4 = X kitit id uynitnok kadiT .b

C = X kitit paites id uynitnoK .c

X | X { lavretni adap uynitnok kadiT .d } 7 ≤

nasululeK airetirK .C

airetirK rokS 1( – )01 toboB ialiN nagnareteK

( fitingoK 3 .ds 1 romon laos ) 5

sulul taraySm ialin lamini

65

isaton silunem naitileteK 1

rudesorp natapeteK 2

nabawaj alumrof natapeteK 1

utkaw natapeteK 1

RIHKA IALIN

03

VI BAB

PUTUNEP

ludum halnaikimeD 102 FKT .TAM – luduj nagned 10 nad timiLsgnuF satiuynitnoK i sid iaseles halet ini nusu ipakgnelid nagned

icnuk atreseb rihka isaulave nupuam fitamrof set ,sagut/nahital aparebeb

awsisaham arap nakparahid ini ludom nautnab nagneD .aynnabawaj

akerem hakapa ,aynisnetepmok nagnabmekrep iridnes uatnamem tapad

eb halet ran - adap nimrecret anamiagabes isnetepmok ikilimem raneb

.muleb uata rajaleb nataigek paites adap nakparahid gnay naujut

laminim nasululek tarays iapacnem halet gnay awsisaham arap igaB

adap aynrajaleb nataigek nakitnehgnem tapad akerem akam ludom ini

.ayntukireb ludom ek naktujnalem nad tapad muleb akij aynkilabeS

ilabmek gnalugnem surah akerem akam ,laminim nasululek ihunemem

iretam naigab adap amaturet aynrajaleb - ayniasaukid muleb gnay iretam

( sulul muleb huggnus hibel surah akerem aynkiabes nad ) - huggnus

nautnab kusamret ada gnay satilisaf naktaafnamem nagned rajaleb malad

.ini hailukatam rotatilisaf iagabes nesod irad

13

AKATSUP RATFAD

seryA knarF , rJ ., 91 48 . : largetnI nad laisnerefiD .suluklaK audeK isidE

:atrakaJ .)nahamejreT( aggnalrE .

.3991 .E ,gizsyerK natujnaL kinkeT akitametaM .)nahamejreT( 2 & 1 ukuB.aidemarG .TP :atrakaJ

,.kkd olisuS namojN .8891 1 diliJ sitilanA irtemoeG nad suluklaK : atrakaJ .aggnalrE

.M ,legeipS .4891 .R natujnaL akitametaM aggnalrE :atrakaJ .)nahamejreT(

.6891 .A.K ,duortS utnu akitametaM kinkeT k .)nahamejreT( :atrakaJ.aggnalrE