Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - P.S. Problem Solving - Page 239: 9b


$(f o g)^{-1} (x)=\dfrac{x}{4}-6$

Work Step by Step

We have $f(g(x))=f(x+6)$ or, $=4(x+6)$ or, $=4x+(6)(4)$ or, $y=4x+24$ Interchanging $x$ and $y$: $x=4y +24$ $\implies \dfrac{x}{4}=y+6$ or, $y=\dfrac{x}{4}-6$ Replace $y$ with $(f o g)^{-1} (x)$ $(f o g)^{-1} (x)=\dfrac{x}{4}-6$
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