Find the domain and range of the function `f(x)="sin"^(-1)(x^(2))/(2)`

Explanation

To find the domain and range of the function \( f(x) = \sin^{-1}\left(\frac{x^2}{2}\right) \), we will follow these steps:

### Step 1: Determine the domain of \( f(x) \)

The function \( \sin^{-1}(y) \) is defined for \( y \) in the interval \([-1, 1]\). Therefore, we need to ensure that the argument of the inverse sine function, which is \( \frac{x^2}{2} \), lies within this interval.

1. Set up the inequality:
\[
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