A) \[\{x:1\le x\le 2\}\]
B) \[\{x:1\le x\le 3\}\]
C) \[\{x:-1\le x\le 2\}\]
D) \[\left\{ x:\frac{1}{2}\le x\le 2 \right\}\]
E) \[\left\{ x:-\frac{1}{2}\le x\le 2 \right\}\]
Correct Answer: D
Solution :
We have, \[f(x)={{\sin }^{-1}}({{\log }_{2}}x)\] \[\therefore \]\[-1\le {{\log }_{2}}x\le 1\] \[(\because -1\le {{\sin }^{-1}}x\le 1)\] \[\Rightarrow \] \[{{2}^{-1}}\le x\le {{2}^{1}}\] \[\Rightarrow \] \[\frac{1}{2}\le x\le 2\] \[\therefore \]Domain of the function\[=\left\{ x:\frac{1}{2}\le x\le 2 \right\}\]
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