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] $