Question Number 1454 by 123456 last updated on 06/Aug/15
$$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R},\:\mathrm{if}\:\left({f}\bullet{f}\right)\left({x}\right)\:\mathrm{is}\:\mathrm{continuous} \\ $$$$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{continous}. \\ $$
Commented by 123456 last updated on 07/Aug/15
$${f}\left({x}\right)=\begin{cases}{\mathrm{3},{x}>\mathrm{0}}\\{\mathrm{2},{x}=\mathrm{0}}\\{\mathrm{1},{x}<\mathrm{0}}\end{cases} \\ $$
Commented by prakash jain last updated on 08/Aug/15
$${f}\left({x}\right)=\frac{\mathrm{1}}{{x}} \\ $$