The domain of the function defined by f(x) = sin^-1 √(x - 1) is

The correct answer is Option (1) → $[1, 2]$ ##

$∵f(x) = \sin^{-1} \sqrt{x - 1}$

$∴0 \le x - 1 \le 1 \quad [∵\sqrt{x - 1} \ge 0 \text{ and } -1 \le \sqrt{x - 1} \le 1]$

$\Rightarrow 1 \le x \le 2$

$∴x \in [1, 2]$