The range of the provided inverse sine function in terms of <em>x</em>, and <em>y </em>y = sin-1x is [-π/2, π/2].
<h3>What is the range of the function?</h3>
Range of a function is the set of all the possible output values which are valid for that function.
The trigonometry function given in the problem is,
![y = \sin^{-1}x](https://tex.z-dn.net/?f=y%20%3D%20%5Csin%5E%7B-1%7Dx)
The above function can be written as,
![\sin y = x](https://tex.z-dn.net/?f=%5Csin%20y%20%3D%20x)
The above function is the arc of sine function. The domain of arc of sine ranges from -1 to 1.
![-1\leq x\leq1](https://tex.z-dn.net/?f=-1%5Cleq%20x%5Cleq1)
This is the domain of the inverse of sine function. In the attached image below, the graph of inverse sine function is plotted. The range of this function is,
![-\dfrac{\pi}{2}\leq x\leq\dfrac{\pi}{2}](https://tex.z-dn.net/?f=-%5Cdfrac%7B%5Cpi%7D%7B2%7D%5Cleq%20x%5Cleq%5Cdfrac%7B%5Cpi%7D%7B2%7D)
Thus, the range of the provided inverse sine function in terms of <em>x</em>, and <em>y </em>y = sin-1x is [-π/2, π/2].
Learn more about the range of the function here;
brainly.com/question/2264373