Warm – up # 5 C (0, –1) V (0, 2) V (0, –4) F (0, 4) F (0, –6)
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Warm – up # 5 1. Opens: y a = 3 b = 4 c = C (0, –1) V (0, 2) V (0, –4) F (0, 4) F (0, –6)
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Transcript of Warm – up # 5 C (0, –1) V (0, 2) V (0, –4) F (0, 4) F (0, –6)
Warm – up # 5 1.
Opens: ya = 3 b = 4 c =
C (0, –1)V (0, 2)V (0, –4)F (0, 4)F (0, –6)
Homework LogWed
12/2
Lesson 4 – 6
Learning Objective: To find inverse of functions
Hw: #407 Pg. 254 #1 – 4 all, 5 – 17 odd, 19, 23, 25, 27
12/2/15 Lesson 4 – 6 Inverse FunctionsAdvanced Math/Trig
Learning Objective
To find inverse of functions
To identify whether functions are inverses
One–to–One FunctionFunction – x values don’t repeat & pass Vertical Line Test
One–to–One Function – A Function whose y–values don’t repeat & passes the HORIZONTAL line test
Function NOT a FunctionFunction FunctionNOT 1 - 1 1 - 1 1 - 1
Inverse FunctionEvery 1–1 function has an inverse function
Switch x & y
is read as “the inverse of f ” or “f inverse”Don’t confuse with negative exponent!
Inverse FunctionTo find Inverse
Replace (or with y
Switch x & y
Solve for y
Replace y with ( or
Find Inverse1. Find an expression for if
Replace with y y = 3x + 6
Switch x & y x = 3y + 6
Solve for y x – 6 = 3y
Replace y with
Graph both and 1.
m = 3 y – int = 6
m = y – int = –2
y = x
g(x)
g –1(x)
Symmetric about line y = x
Verifying/Determining Inverse Function
To verify or determine whether two functions are inverses, show that
for all x in domain of
for all x in domain of
BOTH must be true if they are inverses of each other
Find InverseFind an expression for & if f is 1–1
If f is 1–1, verify &2.
Solve for y
Replace y with
f is not 1–1 so it does not have an inverse
Find Inverse3. 3x – 2y = 6
3x – 6 = 2y
It’s a straight line, (not horizontal), so it’s 1–1
Verify Inverses3.
Show
=() – 3
= x + 3 – 3
= x
Show
=() + 2
= x – 2 + 2
= x
Find Inverse4.
Parabola that opens up
f is not 1–1 so it does not have an inverse
Find Inverse5.
It is 1–1
Verify Inverses5.
Show
=
= x – 1 + 1
= x
Show
=
=
= x
Determine if f & g are inverses of each other
6.
Show
= = = =
= = = =
f and g are NOT inverses of each other!
Determine if f & g are inverses of each other
7.
Show
=
Show
= =
f and g are NOT inverses of each other!
= x + 2 – 2
= x
Determine if f & g are inverses of each other
8.
Show
=
Show
= =
f and g ARE inverses of each other
= x – 3 + 3
= x
Determine if f & g are inverses of each other
9.
Show
=
Show
=
f and g are inverses of each other
= = =
= = = x
Ticket Out the Door
Determine if
and
are inverses of each other
Homework
#407 Pg. 254 1 – 4 all, 5 – 17 odd, 19, 23, 25, 27
