Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Do Now: Find f(g(x)) and Do Now: Find f(g(x)) and g(f(x)). g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x 2 2 + 2 + 2

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Transcript of Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Page 1: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Do Now: Find f(g(x)) and g(f(x)).Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = xf(x) = x + 4, g(x) = x22 + 2 + 2

Page 2: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Algebra IIAlgebra II

6.4: Use Inverse Functions6.4: Use Inverse FunctionsHW: p.442 (4-10 even, 16, 18, 22, HW: p.442 (4-10 even, 16, 18, 22,

26)26)

Page 3: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Inverse RelationsInverse Relations An inverse relation interchanges An inverse relation interchanges

the input and output values (the the input and output values (the x and y) of the original relation.x and y) of the original relation.

This means the domain and range This means the domain and range also change, since the domain is your also change, since the domain is your input and the range is your output.input and the range is your output.

Page 4: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Find the inverse of the Find the inverse of the relation.relation.

y = 3x – 5y = 3x – 5

y = 5x + ½ y = 5x + ½

Page 5: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Find the inverse of the Find the inverse of the function.function.

f(x) = xf(x) = x33 – 2 – 2

f(x)= f(x)=

Inverse FunctionsInverse Functions

If both the relation and the If both the relation and the inverse of the relation are inverse of the relation are functions, then they are called functions, then they are called inverse functions.inverse functions.

Page 7: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Inverse functionsInverse functions

Functions Functions ff and and gg are inverses of are inverses of each other provided:each other provided:

f f ((g g ((x x )))) = = xx and and g g ((f f ((x x )))) = = xx

Page 8: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Verify that f and g are inverse Verify that f and g are inverse functions.functions.

f(x) = x + 4, g(x) = x – 4f(x) = x + 4, g(x) = x – 4

Page 9: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Verify that f and g are inverse Verify that f and g are inverse functions.functions.

f(x) = , g(x) =f(x) = , g(x) =

Page 10: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Sketch the graph of the inverse Sketch the graph of the inverse relation. Are these inverse relation. Are these inverse

functions?functions?

Page 11: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Sketch the graph of the inverse Sketch the graph of the inverse relation. Are these inverse relation. Are these inverse

functions?functions?

Page 12: Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x 2 + 2 f(x) = x + 4, g(x) = x 2 + 2.

Find the inverse of the Find the inverse of the function.function.

f(x) = xf(x) = x44 – 2 – 2

f(x)= f(x)=

Lösungsvorschläge zu ausgewählten Übungsaufgaben aus ... · x −0 = √ x gegen 0, d.h. g ist in 0 differenzierbar mit g ... Es gelte dort f(x)g(x) = x sowie f(0) = g(0) = 0.

1.8 Combinations of Functions: Composite Functions. 84-92.pdf · f g x f x g x 2x 1 x2 2x 1 x2 4x f x 2x 1 g x x2 2x 1, f g x. ... Sum, Difference, Product, and Quotient of Functions

M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

1. f( g(x)) = ____ for g(x) = 2x + 1 and f(x) = 4x, if x = 3 2. (f + g)(x) = ____ for g(x) = 3x 2 + 2x and f(x) = 3x + 1 3. (f/g)(x) = ______ for f(x)

2: x 1 x f x = f x f ={0,1 g x =g x g 0,1 - CICESEusuario.cicese.mx/~jasan/ClaseSCD5.pdf · 2008-02-22 · 2l se llama conjugado de . Si es una raiz de x 2m−1 1 entonces: 2m−1

f,g f f. f - askisopolis.gr · f x 3 4 2 5 xx ... 3f 101 2f 1001 f 10001 log18 6 28. f x ln e 1 x g x ln 2e 2 1x . f,g. f,g f 2x g x 1 ! . g 1 x f x ln2 29. f x log x 1 log x 2x 2

Definition: Let f and g be two functions such that x g x f g f1.9 Inverse Functions Definition: Let f and g be two functions such that f g x x for every x in the domain of g and g

lawhonmath.weebly.com · Web view1. f x =4x-1, g x = 6+7x 2. f x =5x+2, g x = x 2 -14x . 3. f x = x 2 -2x+1, g x =8-3 x 2 4. f x = x 2 +3, g x = 5+ x 2 . Compute f -1 (x) of the following

$Math 121 Final Review · 2020. 11. 21. · Math 121 Final Review 1 Pre-Calculus 1. Let f(x) = (x+ 2)2 and g(x) = x3, nd: a. (f+ g)(x) b. (fg)(x) c. (f=g)(x) d. (f g)(x) e. (g f)(x)$