If f(x)
Question:

If $f(x)=\sin ^{2} x$ and the composite function $g(f(x))=|\sin x|$, then $g(x)$ is equal to

(a) $\sqrt{x-1}$

(b) $\sqrt{x}$

(c) $\sqrt{x+1}$

(d) $-\sqrt{x}$

Solution:

(b)

If we take $g(x)=\sqrt{x}$, then

$g(f(x))=g\left(\sin ^{2} x\right)=\sqrt{\sin ^{2} x}=\pm \sin x=|\sin x|$

So, the answer is (b).

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