Chapter 7: Transcendental Functions - Section 7.1 - Inverse Functions and Their Derivatives - Exercises 7.1 - Page 372: 20

$$ f^{-1}(x)=-\sqrt x $$

Given $$ y=x^{2}$$ Solve for $x$: \begin{aligned} & y=x^{2}\\ & \Rightarrow x^{2}=y \\ &\Rightarrow x=-\sqrt{y}, \ \ \ \text{Since}, x\leq 0 \\ \text{Switch $ x $ and $ y $}\\ &y=-\sqrt{x}=f^{-1}(x) \end{aligned}