Mathematics - Functions Question with Solution | TestHub

$\begin{array}{rl}& \text{ Given that, }f(x)=[x]\text{ and }g(x)=|x|\\ & \text{ Now, }\mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)=\mathrm{g}\left(\frac{8}{5}\right)=\left[\frac{8}{5}\right]=1\end{array}$ and $\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)=\mathrm{g}\left(\left[-\frac{8}{5}\right]\right)=\mathrm{g}(-2)=|-2|=2$ $\therefore \mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)-\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)=1-2=-1$