The domain of the function $y = \sin^{-1}(x-1) + \cos^{-1}\sqrt{x-1}$ is:

$[1, 2]$

The correct answer is Option (3) → $[1, 2]$

The function is $y = \sin^{-1}(x - 1) + \cos^{-1}(\sqrt{x - 1})$

For $\sin^{-1}(x - 1)$ to be defined: $-1 \leq x - 1 \leq 1 \Rightarrow 0 \leq x \leq 2$

For $\cos^{-1}(\sqrt{x - 1})$ to be defined: $0 \leq \sqrt{x - 1} \leq 1 \Rightarrow 0 \leq x - 1 \leq 1 \Rightarrow 1 \leq x \leq 2$

Common domain: $x \in [1, 2]$