Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.1 Composite Functions - 5.1 Assess Your Understanding - Page 255: 45

Answer

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Work Step by Step

We are given the functions: $f(x)=ax+b$ $g(x)=\dfrac{1}{a}(x-b)$ Determine $f\circ g$: $(f\circ g)(x)=f(g(x))=f\left(\dfrac{1}{a}(x-b)\right)=a\cdot \dfrac{1}{a}(x-b)+b=x-b+b=x$ Determine $g\circ f$: $(g\circ f)(x)=g(f(x))=g\left(ax+b\right)=\dfrac{1}{a}(ax+b-b))=\dfrac{1}{a}\cdot ax=x$ We got: $(f\circ g)(x)=(g\circ f)(x)=x$
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