Question

The domain of $f\left(x\right)=\sqrt{{\sin }^{-1}\left({\log }_{9}x\right)}$ is

• A. $\left[0\right]$
• B. $[1,9]$
• C. $[0,3]$
• D. $[0,\infty )$

Answer 1

The correct option is B $[1,9]$

${\sin }^{-1}x$ is defined if $x\in [-1,1]$
But as ${\sin }^{-1}$ is under square root, it has to be positive
$\Rightarrow 0\le {\log }_{9}x\le 1$
$\Rightarrow 1\le x\le 9$