Question

The domain of $f\left(x\right)=\sqrt{{\sin }^{-1}\left({\log }_{2}x\right)}$ is

Answer 1

Find the domain of ${\sin }^{-1}\left[lo{g}_2\left(\frac{x}{2}\right)\right]$

$lo{g}_2\left(\frac{x}{2}\right)$ is defined for $\frac{x}{2}>0$

$x>0$

Also domain of ${\sin }^{-1}x$ is $[-1,1]$

when $x=1$ then $lo{g}_2\left(\frac{x}{2}\right)$ becomes $-1$

when $x=4$ then $lo{g}_2\left(\frac{x}{2}\right)$ becomes $1$

so, domain $[1,4]$