Intermediate Algebra (6th Edition)

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

Chapter 9 - Review: 25

Answer

$ f^{-1}(x)=\sqrt[3] (x+5)$

Work Step by Step

We are given the function, $f(x)=x^{3}-5$. First, we must replace $f(x)$ with y. $y=x^{3}-5$ Next, interchange x and y. $x=y^{3}-5$ Next, solve for y by adding 5 to both sides. $y^{3}=x+5$ Take the cube root of both sides. $\sqrt[3] (y^{3})=y=\sqrt[3] (x+5)$ Finally, replace y with $f^{-1}(x)$. $ f^{-1}(x)=\sqrt[3] (x+5)$
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