Mathematics - Functions Question with Solution | TestHub

Given, $f(x)=[x]$ and $g(x)=|x|$ Now, $\begin{array}{c}f\left(\frac{-8}{5}\right)=\left[-\frac{8}{5}\right]=-2\dots (i)\\ g\left(\frac{8}{5}\right)=\left|\frac{8}{5}\right|=\frac{8}{5}\dots (ii)\end{array}$ Now, $f\left(g\left(\frac{8}{5}\right)\right)-g\left(f\left(-\frac{8}{5}\right)\right)=f\left(\frac{8}{5}\right)-g(-2)$ By Eqs. (i) and (ii), $\begin{array}{rl}& =\left[\frac{8}{5}\right]-|-2|\\ & =1-2\\ & =-1\end{array}$