What is the domain of $\sec^{-1} x$?

Explanation

1. 01

   $\sec \theta = \frac{1}{\cos \theta}$, and $\lvert\cos \theta\rvert \le 1$, so $\lvert\sec \theta\rvert \ge 1$.

2. 02

   So $\sec^{-1} x$ is defined for $\lvert x \rvert \ge 1$, that is $\mathbb{R} - (-1, 1)$.