Question:
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:
To Find: The range of $\sin ^{-1} x$
Here,the inverse function is given by $y=f^{-1}(x)$
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 $y=\sin ^{-1}(x)$
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
$\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$