Mathematics - Functions Question with Solution | TestHub

We have, $fog(-x)=f[g(-x)]=f[-g(x)]$ $(\because g$ is odd $)$ $\begin{array}{l}=\mathrm{f}[\mathrm{g}(\mathrm{x})](\because \mathrm{fis}\text{ even })\\ =\mathrm{fog}(\mathrm{x})\forall \mathrm{x}\in \mathrm{R}\end{array}$ $\therefore$ fog is an even function.