Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Review: 26

Answer

$ f^{-1}(x)=x^{3}-2$

Work Step by Step

We are given the function, $f(x)=\sqrt[3] (x+2)$. First, we must replace $f(x)$ with y. $y=\sqrt[3] (x+2)$ Next, interchange x and y. $x=\sqrt[3] (y+2)$ Next, cube both sides. $x^{3}=(\sqrt[3] (y+2))^{3}$ $x^{3}=y+2$ Next, subtract 2 from both sides. $y=x^{3}-2$ Finally, replace y with $f^{-1}(x)$. $ f^{-1}(x)=x^{3}-2$
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