   Chapter 1.3, Problem 50E ### 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

# Express the function in the form f ◦ g ◦ h.50. H ( x ) = 2 + | x | 8

To determine

To express: The function H(x)=2+|x|8 in the form of (fgh)(x) .

Explanation

Given:

The composite function is R(x)=x1 .

Calculation:

Name the expression |x| as h(x)=|x| .

Thus, H(x)=2+h(x)8 .

Replace h(x) by x to obtain the expression for g(x) .

Therefore, H(x)=2+x8 .

Name the expression 2+x as g(x)=2+x .

Thus, H(x)=g(x)8 .

Similarly, replace g(x) by x to obtain the expression for f(x) .

Therefore, f(x)=x8 .

Hence, it can be concluded that H(x)=2+|x|8 can be expressed as H(x)=f(g(h(x))), where f(x)=x8,g(x)=2+x and  h(x)=|x| .

Verification:

The composite function (fgh)(x) is defined as follows.

(fgh)(x)=f(gh)(x)

First find the composite function of (gh)(x)

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