What is the domain of $\sin^{-1}(x^{2})$?

Explanation

1. 01

   The input of the inverse function must lie in its domain: $-1 \le x^{2} \le 1$.

2. 02

   $x^{2} \ge 0$ always, so it means $x^{2} \le 1$: $-1 \le x \le 1$.