Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Review - Exercises - Page 234: 97

Answer

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

Work Step by Step

$f(x)=(x+1)^{3}$ Substitute $f(x)$ by $y$: $y=(x+1)^{3}$ Solve for $x$: $\sqrt[3]{y}=x+1$ $x+1=\sqrt[3]{y}$ $x=\sqrt[3]{y}-1$ Interchange $x$ and $y$: $y=\sqrt[3]{x}-1$ Substitute $y$ by $f^{-1}(x)$: $f^{-1}(x)=\sqrt[3]{x}-1$
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