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: 34

Answer

$f^{-1}(x)=x^{3}-1$

Work Step by Step

$f(x)=\sqrt[3]{x+1}$ Replace $f(x)$ with $y$: $y=\sqrt[3]{x+1}$ Interchange $x$ and $y$: $x=\sqrt[3]{y+1}$ Let's solve for $y$. Start by cubing both sides: $x^{3}=(\sqrt[3]{y+1})^{3}$ $x^{3}=y+1$ Take the $1$ to the left side: $x^{3}-1=y$ Replace $y$ with $f^{-1}(x)$: $f^{-1}(x)=x^{3}-1$
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