The domain of the function $f(x) = \sin^{-1}(x)$ is

$\sin^{-1}$ is the inverse of sine restricted to $[-\tfrac{\pi}{2}, \tfrac{\pi}{2}]$, where sine takes every value in $[-1,1]$ exactly once. So the inverse is defined precisely on $x \in [-1, 1]$. **Option D is the *range* of $\sin^{-1}$, not the domain.**