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).