A) \[[1,\,\,9]\]
B) \[[-1,\,\,9]\]
C) \[[-9,\,\,1]\]
D) \[[-9,\,\,-1]\]
Correct Answer: A
Solution :
Key Idea: The domain of\[{{\sin }^{-1}}x\]is\[[-1,\,\,1]\]. \[f(x)={{\sin }^{-1}}\left( {{\log }_{3}}\left( \frac{x}{3} \right) \right)\]exists, if \[-1\le {{\log }_{3}}\left( \frac{x}{3} \right)\le 1\] \[\Rightarrow \] \[{{3}^{-1}}\le \frac{x}{3}\le {{3}^{1}}\] \[\Rightarrow \] \[1\le x\le 9\Rightarrow \]domain is\[[1,\,\,9]\]
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