Question

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

• A. $[1,2]$
• B. $[-1,1]$
• C. $[0,1]$
• D. None of these

Answer 1

Answer: (A)

$\frac{-\pi }{2}\le {\sin }^{-1}\sqrt{x-1}\le \frac{\pi }{2}$
$\Rightarrow -1\le \sqrt{x-1}\le 1$
$\Rightarrow 0\le x-1<1$
$\Rightarrow 1\le x\le 2$
$\therefore$ Domain of $f(x)$ is $[1,2]$