Let \(f(x)=x^2\) and \(g(x)=\sin x\) for all \(x \in R\). Then, the set of all \(x\) satisfying \((\) fogogof \()(x)=(\operatorname{gogof})(x)\), where \((f \circ g)(x)=f(g(x))\) is

\(f(x)=x^2, g(x)=\sin x\)
\((g \circ f)(x)=\sin x^2\)
go(gof) \((x)=\sin \left(\sin x^2\right)\)
\((f \circ g \circ g \circ f)(x)=\left(\sin \left(\sin x^2\right)\right)^2\)
Again, \((g \circ f)(x)=\sin x^2\)
(gogof) \((x)=\sin \left(\sin x^2\right)\)
Given, \((\) fogogof \()(x)=(\) gogof \()(x)\)
\(\Rightarrow \quad\left(\sin \left(\sin x^2\right)\right)^2=\sin \left(\sin x^2\right)\)
\(\Rightarrow \sin \left(\sin x^2\right)\left\{\sin \left(\sin x^2\right)-1\right\}=0\)
\(\Rightarrow \sin \left(\sin x^2\right)=0\) or \(\sin \left(\sin x^2\right)=1\)
\(\Rightarrow \sin x^2=0\) or \(\sin x^2=\frac{\pi}{2}\)
\(\therefore \quad x^2=n \pi\)
(i.e. not possible as \(-1 \leq \sin \theta \leq 1\) )