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Question

If f(g(x))=|sin x| and g(f(x))=sin2 x, then

A
f(x) and g(x) are both periodic functions.
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B
f(x) is periodic but g(x) is not a periodic function
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C
f(x) is not periodic while g(x) is a periodic function
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D
f(x) and g(x) are both non-periodic functions.
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Solution

The correct option is C f(x) is not periodic while g(x) is a periodic function
We know that a2=|a|
f(g(x))=|sin x|=sin2x
f(x)=x; g(x)=sin2x
f(x) is non periodic and g(x) is periodic.

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