A) \[\left[ \frac{1}{2},\frac{1}{4} \right]\]
B) \[[-1,3]\]
C) \[[1,4]\]
D) \[[0,1]\]
Correct Answer: C
Solution :
Since, domain of\[{{\sin }^{-1}}x\]is\[[-1,1]\] \[\therefore \]For\[{{\sin }^{-1}}\left( {{\log }_{2}}\frac{x}{2} \right)\] \[-1\le {{\log }_{2}}\frac{x}{2}\le 1\] \[\Rightarrow \] \[{{2}^{-1}}\le \frac{x}{2}\le 2\] \[\Rightarrow \] \[1\le x\le 4\] \[\therefore \]Domain is [1, 4].
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