This question is based on the trigonometry. Therefore, the correct option is C, i,e. [tex][\dfrac{-\pi}{2} ,\dfrac{\pi}{2}][/tex] is the range of [tex]Sin^{-1} x[/tex].
Given:
Function is y = [tex]Sin^{-1} x[/tex].
We need to determined the range of the function y = [tex]Sin^{-1} x[/tex].
As we know that,
Domain of [tex]Sin^{-1} x[/tex] is −1 ≤ [tex]Sin^{-1} x[/tex] ≤ 1.
By using the graph of y = [tex]Sin^{-1} x[/tex] . we would be find the range.
We observe in graph that,
The upper limit of graph of given function is [tex]+\dfrac{\pi}{2}[/tex].
And, the lower limit of graph of given function is [tex]-\dfrac{\pi}{2}[/tex].
Thus, the range of y = [tex]Sin^{-1} x[/tex] function is [tex][\dfrac{-\pi}{2} ,\dfrac{\pi}{2}][/tex].
Therefore, the correct option is C, i,e. [tex][\dfrac{-\pi}{2} ,\dfrac{\pi}{2}][/tex] is the range of [tex]Sin^{-1} x[/tex].
For more details, prefer this link:
https://brainly.com/question/15274395
