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

Explanation

1. 01

   Each inverse function must get an input from its domain: $-1 \le x^{2} - 1 \le 1$.

2. 02

   So $0 \le x^{2} \le 2$, so $-\sqrt{2} \le x \le \sqrt{2}$.