Question

If $f\left(x\right)={\sin }^{2}x$ and the composite function $g\left(f\left(x\right)\right)=\left|\sin x\right|$, then g(x) is equal to
(a) $\sqrt{x-1}$
(b) $\sqrt{x}$
(c) $\sqrt{x+1}$
(d) $-\sqrt{x}$

Answer 1

(b)

$$\begin{gathered} \text{If we take}g\left(x\right)=\sqrt{x},\text{then} \\ g\left(f\left(x\right)\right)=g\left({\sin }^{2}x\right)=\sqrt{{\sin }^{2}x}=\pm \sin x=\left|\sin x\right| \end{gathered}$$

So, the answer is (b).