alleryThe domain of the function $f(x) = \sin^{-1}(x)$ is
A$[-\tfrac{\pi}{2}, \tfrac{\pi}{2}]$
B$\mathbb{R}$
C$[-1, 1]$
D$[0, \pi]$
Answer & Solution
Correct answer: C. $[-1, 1]$
$\sin^{-1}$ 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.**
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