Question

If
(a)
(b)
(c)
(d) f and g cannot be determined.

Answer 1

If we solve it by the trial-and-error method, we can see that (a) satisfies the given condition.
From (a):
$$\begin{gathered} f\left(x\right)={\sin }^{2}x\text{and}g\left(x\right)=\sqrt{x} \\ \Rightarrow f\left(g\left(x\right)\right)=f\left(\sqrt{x}\right)={\sin }^2\sqrt{x}={\left(\sin \sqrt{x}\right)}^2 \end{gathered}$$
So, the answer is (a).