Mark the tick against the correct answer in the following: Range of \sin ^{-1} x is
A. \left[0, \frac{\pi}{2}\right]
B. [0, \pi]
C. \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]
D. None of these
Mark the tick against the correct answer in the following: Range of \sin ^{-1} x is
A. \left[0, \frac{\pi}{2}\right]
B. [0, \pi]
C. \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]
D. None of these

Solution:

Option() is correct.
To Find: The range of \sin ^{-1} x
Here,the inverse function is given by \mathrm{y}=\mathrm{f}^{-1}(x)
The graph of the function y=\sin ^{-1}(x) can be obtained from the graph of Y=\sin x by interchanging x and y axes.i.e, if (a, b) is a point on Y=\sin x then (b, a) is The point on the function \mathrm{y}=\sin ^{-1}(x)
Below is the Graph of range of \sin ^{-1}(x)

From the graph, it is clear that the range of \sin ^{-1}(x) is restricted to the interval
\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]