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  4. Domain of the function f(x)= sin -1( log 2x) in the set of real numbers is:

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Q. Domain of the function $ f(x)={{\sin }^{-1}}({{\log }_{2}}x) $ in the set of real numbers is:

KEAMKEAM 2003

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\} $