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  4. The domain of sin -1( (2x+1/3) ) is:

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Q. The domain of $ {{\sin }^{-1}}\left( \frac{2x+1}{3} \right) $ is:

KEAMKEAM 2001

Solution:

Let $ y={{\sin }^{-1}}\left( \frac{2x+1}{3} \right) $ $ \therefore $ $ -1\le \frac{2x+1}{3}\le 1 $ $ (\because -1\le {{\sin }^{-1}}x\le 1) $ $ \Rightarrow $ $ -3\le 2x+1\le 3 $ $ \Rightarrow $ $ -4\le 2x\le 2 $ $ \Rightarrow $ $ -2\le x\le 1 $ $ \therefore $ $ x\in [-2,1] $