College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Review - Exercises: 97

Answer

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

Work Step by Step

We are given: $f(x)=(x+1)^{3}$ To find the inverse function, we switch $x$ and $y$ and solve for $y$: $y=(x+1)^{3}$ $x=(y+1)^{3}$ $\sqrt[3]{x}=y+1$ $\sqrt[3]{x}-1=y$ Thus the inverse is: $f^{-1}(x)=\sqrt[3]{x}-1$
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