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Question
If \[f\left( x \right) = \sin^2 x\] and the composite function \[g\left( f\left( x \right) \right) = \left| \sin x \right|\] then g(x) is equal to
Options
\[\sqrt{x - 1}\]
\[\sqrt{x}\]
\[\sqrt{x + 1}\]
\[- \sqrt{x}\]
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Solution
(b) \[\text{If we takeg}\left( x \right) = \sqrt{x}, \text{then}\]
\[g\left( f\left( x \right) \right) = g\left( \sin^2 x \right) = \sqrt{\sin^2 x} = \pm \sin x = \left| \sin x \right|\]
So, the answer is (b).
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