A) \[0\le x\le 1\]
B) \[0\le x\le 4\]
C) \[1\le x\le 4\]
D) \[4\le x\le 6\]
Correct Answer: C
Solution :
Given function, \[f(x)={{\sin }^{-1}}\left[ {{\log }_{2}}\left( \frac{x}{2} \right) \right]\] Since, \[-1\le \sin x\le -1\] \[\Rightarrow \] \[-1\le {{\log }_{2}}\left( \frac{x}{2} \right)\le 1\] \[\Rightarrow \] \[{{2}^{-1}}\le x/2\le {{2}^{2}}\] \[\Rightarrow \] \[{{2}^{0}}\le x\le {{2}^{2}}\] \[\Rightarrow \] \[1\le x\le 4\] Required domain is \[x\in [11,4]\].
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