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

$f(x) = \sin^2 x, g(x) = \sqrt{x}$ $f(x) = \sin x, g(x) = |x|$ $f(x) = x^2, g(x) = \sin \sqrt{x}$ f and g cannot be determined

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

We have, $f(g(x))=(\sin\sqrt{x})^2$ and, $g(f(x))=|\sin x|=\sqrt{\sin^2x}$ $⇒g(x) = \sqrt{x}$ and $f(x) = (\sin x)^2$