Question

The domain of ${\sin }^{-1}\left({\log }_{3}x\right)$ is:

• A. $[-1,1]$
• B. $[0,1]$
• C. $[0,\infty ]$
• D. $R$
• E. $\left[\frac{1}{3},3\right]$

Answer 1

Answer: (E)

For domain of ${\sin }^{-1}\left({\log }_{3}x\right)$
$\therefore$ $-1\le {\log }_{3}x\le 1$
$\Rightarrow$ $3^{-1}\le x\le 3$
$\therefore$ Domain of ${\sin }^{-1}({\log }_{3}x)=\left[\frac{1}{3},3\right]$