Mathematics - Functions Question with Solution | TestHub

From the given information we can conclude
$g\left(S\right)=\left[-\mathrm{2,2}\right]$, So,$f\left(g\right(S\left)\right)=\left[0, 4\right]=S$
And$f\left(S\right)=\left[0, 16\right]\Rightarrow f\left(g\left(S\right)\right)\ne f\left(S\right)$
Also,$g\left(f\left(S\right)\right)=\left[-4, 4\right]\ne g\left(S\right)$
So,$g\left(f\left(S\right)\right)\ne S$
Hence,$g\left(f\left(S\right)\right)=g\left(S\right)$is not true.