A) \[[2,12]\]
B) \[[-1,1]\]
C) \[\left[ \frac{1}{3},24 \right]\]
D) \[\left[ \frac{2}{3},24 \right]\]
E) \[[6,24]\]
Correct Answer: E
Solution :
\[\because \] \[-1\le {{\sin }^{-1}}x\le 1\] \[\Rightarrow \] \[-1\le {{\log }_{2}}\frac{x}{12}\le 1\] \[\Rightarrow \] \[{{2}^{-1}}\le \frac{x}{12}\le {{2}^{1}}\] \[\Rightarrow \] \[6\le x\le 24\] \[\Rightarrow \] Required domain = [6, 24]
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