Find the domain of `f(x)=sin^(-1)(-x^2)dot`

Explanation

To find the domain of the function \( f(x) = \sin^{-1}(-x^2) \), we need to determine the values of \( x \) for which the expression inside the sine inverse function is valid. The sine inverse function, \( \sin^{-1}(y) \), is defined for \( y \) in the interval \([-1, 1]\). Therefore, we need to ensure that:

\[ -1 \leq -x^2 \leq 1 \]

### Step 1: Solve the inequality \( -x^2 \leq 1 \)

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