Decomposing a Composite FunctionIn Exercises 49–56, find two functions f andg such that ( f ∘ g)(x) = h(x). (There are manycorrect answers.)49. h(x) = (2x + 1)2 50. h(x) = (1 − x)351. h(x) = √3 x2 − 4 52. h(x) = √9 − x53. h(x) = 1x + 2 54. h(x) = 4(5x + 2)255. h(x) = −x2 + 34 − x256. h(x) = 27x3 + 6x10 − 27x

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 38WE
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Decomposing a Composite Function
In Exercises 49–56, find two functions f and
g such that ( f ∘ g)(x) = h(x). (There are many
correct answers.)
49. h(x) = (2x + 1)2 50. h(x) = (1 − x)3
51. h(x) = √
3 x2 − 4 52. h(x) = √9 − x
53. h(x) = 1
x + 2 54. h(x) = 4
(5x + 2)2
55. h(x) = −x2 + 3
4 − x2
56. h(x) = 27x3 + 6x
10 − 27x

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