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

Explanation

1. 01

   $\cos^{-1} x$ needs $-1 \le x \le 1$; $\sec^{-1} x$ needs $x \le -1$ or $x \ge 1$.

2. 02

   The sum needs both, and only the ends $x = -1$ and $x = 1$ satisfy both: the domain is $\{-1, 1\}$.