If fog = |sin x| and $gof = sin^2\sqrt{x}$ then f(x) and g(x) are:

$f(x) =\sqrt{sinx}$, $g(x) = x^2$ f(x) = |x|, g(x) = sin x $f(x) = \sqrt{x}$, $g(x) = sin^2x$ $f(x) = sin \sqrt{x}$, $g(x) = x^2$

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

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