Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 50


See the verification below.

Work Step by Step

The functions $f(x)$ and $g(x)$ are known as inverse functions. Thus, we simplify $(f\circ g) (x)=(g\circ f) (x)$ or, $f[g(x)]=g[f(x)]$ as follows: $(f\circ g) (x) =f[g(x)]=f(x-5)=x-5+5 =x$ and $(g\circ f) (x) = g[f(x)]=g(x+5)= x+5-5=x$ Hence, verified.
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