University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.6 - Inverse Functions and Logarithms - Exercises - Page 49: 21

Answer

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

Work Step by Step

$$y=f(x)=x^3-1$$ To find its inverse: 1) Solve for $x$ in terms of $y$: $$y = x^3-1$$ $$x^3=y+1$$ $$x=\sqrt[3]{y+1}$$ 2) Interchange $x$ and $y$: $$y=\sqrt[3]{x+1}$$ Therefore, the inverse of function $y=f(x)=x^3-1$ is the function $y=\sqrt[3]{x+1}$. In other words, $$f^{-1}(x)=\sqrt[3]{x+1}$$
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