Chapter 7: Transcendental Functions - Section 7.1 - Inverse Functions and Their Derivatives - Exercises 7.1 - Page 373: 21

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

Given $$ y=x^{3}-1$$ Find the inverse: \begin{aligned} & y=x^{3}-1\\ & \Rightarrow x^{3}=y+1 \\ &\Rightarrow x=\sqrt[3]{ y+1}, \\\cr & \text{Switch $ x $ and $ y $:} \\ &y=\sqrt[3]{x+1}=f^{-1}(x) \end{aligned}