Chapter 7: Transcendental Functions - Section 7.1 - Inverse Functions and Their Derivatives - Exercises 7.1 - Page 373: 24

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

Given $$ y=x^{\frac{2}{3}} $$ Find the inverse: \begin{aligned} & y=x^{\frac{2}{3}}\\ & \Rightarrow x =y^{\frac{3}{2}} \ \ \ \\ &\text{Switch $ x $ and $ y $}\\ &y=x^{\frac{3}{2}}=f^{-1}(x) \end{aligned}