$\begin{array}{l}Letf\left(x\right)=x^2,x\in R.ForanyA\subseteq R,defineg\left(A\right)=\{x\in R:f\left(x\right)\in A\}.IfS=[0,4],thenwhich\\ oneofthefollowingstatementsisnottrue?\end{array}$

$\begin{array}{l}f\left(x\right)=x^2,g\left(A\right)=\{x\in R:f\left(x\right)\in A\},S=[0,4]\\ g\left(s\right)=[-2,2]\because s=[0,4]\\ \therefore f\left(g\left(s\right)\right)=[0,4]\because g\left(s\right)=[-2,2]\\ andf\left(s\right)=[0,16]\\ g\left(f\left(s\right)\right)=[-4,4]\end{array}$