Find the domain of the function $y = \cos^{-1} (|x - 1|)$.

$[0, 2]$

The correct answer is Option (2) → $[0, 2]$ ##

Since the domain of inverse of cosine function is $[-1, 1]$, finds the domain of the given function as follows:

$-1 \le x - 1 \le 1$

So, $0 \le x \le 2$

And, $-1 \le 1 - x \le 1$

$\Rightarrow 1 \ge x - 1 \ge -1$

So, $2 \ge x \ge 0$

Concludes the domain of $\cos^{-1} (|x - 1|)$ as $[0, 2]$.