Let  $f\left(x\right)=x^2$  and  $g\left(x\right)=\sin x$ for all  $x\in R$ Then ,the set of all  $x$ satisfying  $\left(fogogof\right)\left(x\right)=\left(gogof\right)\left(x\right)$,  where  $\left(fog\right)\left(x\right)=f\left(g\right(x\left)\right),is$

$\begin{array}{l}f\left(x\right)=x^2,g\left(x\right)=\sin x\\ \left(gof\right)\left(x\right)=\sin x^2\\ go\left(gof\right)\left(x\right)=\sin \left(\sin x^2\right)\\ \left(fogogof\right)\left(x\right) = {\left(\sin \left(\sin x^2\right)\right)}^2\\ \left(gof\right)\left(x\right)=\sin x\\ \left(gogof\right)\left(x\right)=\sin \left(\sin x^2\right)\\ \left(fogogof\right)\left(x\right)=\left(gogof\right)\left(x\right)\\ \Rightarrow \left(\sin \right(\sin x^2\left)\right)=\sin \left(\sin x^2\right)\\ \Rightarrow \sin \left(\sin x^2\right)\left\{\sin \right(\sin x^2)-1\}=0\\ \Rightarrow \sin \left(\sin x^2\right)=0 or \left\{\sin \right(\sin x^2)=1\\ x^2=n\pi \\ x=\pm \sqrt{n\pi }\end{array}$