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: 37

Answer

$f^{-1}(x)=\sqrt[3]{x}-2$

Work Step by Step

$f(x)=(x+2)^{3}$ Replace $f(x)$ with $y$: $y=(x+2)^{3}$ Interchange $x$ and $y$: $x=(y+2)^{3}$ Solve for $y$. Begin by taking the cubic root of both sides: $\sqrt[3]{x}=\sqrt[3]{(y+2)^{3}}$ $\sqrt[3]{x}=y+2$ Take the $2$ to the left side: $\sqrt[3]{x}-2=y$ Replace $y$ with $f^{-1}(x)$: $f^{-1}(x)=\sqrt[3]{x}-2$
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