Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.2 - Inverse Functions - Exercise Set - Page 852: 38



Work Step by Step

$f(x)=(x-5)^{3}$ Replace $f(x)$ with $y$: $y=(x-5)^{3}$ Interchange $x$ and $y$: $x=(y-5)^{3}$ Solve for $y$. Start by taking the cubic root of both sides: $\sqrt[3]{x}=\sqrt[3]{(y-5)^{3}}$ $\sqrt[3]{x}=y-5$ Take the $-5$ to the left side: $\sqrt[3]{x}+5=y$ Replace $y$ with $f^{-1}(x)$: $f^{-1}(x)=\sqrt[3]{x}+5$
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