Answer
Domain of $f^{-1}$ = range of $f$ = $[\displaystyle \frac {}{}1,1]$
Range of $f^{-1}$ = domain of $f$ = $[-\displaystyle \frac{\pi}{2},\frac{\pi}{2}]$
Work Step by Step
Follow the instructions:
1. Draw a line through (0,0) and (1,1): $y=x$.
2. Select a few points from the graph of f, and reflect them across $y=x.$
3. Join the new points with a smooth curve: graph of $f^{-1}(x)$
Domain of $f^{-1}$ = range of $f$ = $[\displaystyle \frac {}{}1,1]$
Range of $f^{-1}$ = domain of $f$ = $[-\displaystyle \frac{\pi}{2},\frac{\pi}{2}]$
