Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 422: 86

$\sqrt{r^2-x^2}=f^{-1}(x)$

To find the inverse function we must "swap" $f(x)$ and $x$ and then rearrange the function so that $f^{-1}(x)$ is "alone" on one side of the equation. Hence here: $x=\sqrt{r^2- (f^{-1}(x))^2}\\x^2=r^2 -(f^{-1}(x))^2\\r^2-x^2=(f^{-1}(x))^2\\\sqrt{r^2-x^2}=f^{-1}(x)$