The domain of sin^{-1}x is | vedclass

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Question

(B) The function $f(x) = \sin^{-1}x$ is the inverse of the sine function $y = \sin x$,where the domain of $\sin x$ is restricted to $[-\frac{\pi}{2},

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$[-1, 1]$

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(B) The function $f(x) = \sin^{-1}x$ is the inverse of the sine function $y = \sin x$,where the domain of $\sin x$ is restricted to $[-\frac{\pi}{2}, \frac{\pi}{2}]$ to make it bijective.By the definition of inverse functions,the domain of the inverse function is the range of the original function,and the range of the inverse function is the domain of the original function.Since the range of the sine function $y = \sin x$ is $[-1, 1]$,the domain of its inverse function $\sin^{-1}x$ is $[-1, 1]$.

The domain of $\sin^{-1}x$ is

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