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

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

Inverse Trigonometric Functions

Solution:

$\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<1 $
$ \Rightarrow 1 \leq x \leq 2$
$\therefore $ Domain of $f(x)$ is $[1,2]$