Find the inverse of f(x) = sqrt{r^2 - x^2}, where x is greater than or = to 0 and x is less than or = to r.
The inverse function of f is f.
1. Your equation with it's constraints define a quarter circle with center at the origin placed in the 1st quadrant. If you reflect this quarter circle about the line y = x (first median of the coordinate system) you'll get the same quarter circle.
2. Change x and y in your equation and solve for y:
$\displaystyle y = \sqrt{r^2 - x^2}~\rightarrow~ x= \sqrt{r^2 - y^2}$
$\displaystyle x^2=r^2-y^2~\implies~y^2=r^2-x^2$
The constraints are the same.