If fog = |sin x| and gof = sin^2√x then f(x) and g(x) are:

$fog = f(g(x)) = |sin x| =\sqrt{sin^2x}$.

Also $gof = g(f(x)) = sin^2\sqrt{x}$.

Obviously, = $\sqrt{sin^2x}=\sqrt{g(x)}$

and $sin^2\sqrt{x} = sin^2(f(x))$

i.e. $g(x) = sin^2x$ and $f(x) = \sqrt{x}$.

Hence (C) is the correct answer.