   Chapter 1.3, Problem 63E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 7, find a function f such that f ◦ g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)(b) If f(x) = 3x + 5 and h(x) = 3x2 + 3x + 2, find a function g such that f ◦ g = h.

(a)

To determine

To find: The function f(x) where (fg)(x)=h(x) .

Explanation

The given functions are g(x)=2x+1,h(x)=4x2+4x+7 .

The composite function (fg)(x)=h(x) is defined as follows.

(fg)(x)=h(x)f(g(x))=h(x)

Substitute the expression for g(x) and h(x) .

Thus, f(2x+1)=4x2+4x+7

(b)

To determine

To find: The function g(x) where (fg)(x)=h(x) .

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 