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

Question

The domain of the function defined by $f(x)=\sin ^{-1} \sqrt{x-1}$ is

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Answer

(a): We know, $\frac{-\pi}{2} \leq \sin ^{-1} \sqrt{x-1} \leq \frac{\pi}{2}$
$\Rightarrow-1 \leq \sqrt{x-1} \leq 1 \Rightarrow 0 \leq x-1 \leq 1 \Rightarrow 1 \leq x \leq 2$
$\therefore \quad$ Domain of $f(x)$ is $[1,2]$.

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