Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises - Page 416: 7


$x^{1/3}$ or $\sqrt[3]{x}$

Work Step by Step

To find the equation for $f^{-1}$, replace $f(x)$ with $y$, interchange $x$ and $y$, and solve for $y$. This gives $f^{-1}(x)$. ------------ $ y=x^{3}\qquad$ ... swap x and y $ x=y^{3}\qquad /(...)^{1/3}\quad$... solve for y $x^{1/3}=y$ (RHS:$ (y^{3})^{1/3}=y^{3\cdot\frac{1}{3}}=y^{1}=y)$ $y=f^{-1}(x)=x^{1/3}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.