A) [1, 9]
B) [-1, 9]
C) [-9, 1]
D) [-9,-1]
Correct Answer: A
Solution :
Domain of \[{{\sin }^{-1}}x=[-1,1]\] and range of \[{{\sin }^{-1}}x=\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]. Since, domain of \[{{\sin }^{-1}}x=[-1,1]\] \[\therefore \] \[-1\le {{\log }_{3}}\left( \frac{x}{3} \right)\le 1\] \[\Rightarrow \] \[{{3}^{-1}}\le \frac{x}{3}\le 3\] \[\Rightarrow \] \[1\le x\le 9\] \[\therefore \] Domain of \[{{\sin }^{-1}}\left[ {{\log }_{3}}\left( \frac{x}{3} \right) \right]\]is [1, 9].
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