Question Number 30563 by abdo imad last updated on 23/Feb/18
$${let}\:{f}\left({x}\right)=\mid{x}−\mathrm{2}\:\left[\frac{{x}+\mathrm{1}}{\mathrm{2}}\right]\mid \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\:{is}\:{periodic} \\ $$$$\left.\mathrm{2}\right)\:{simplify}\:{f}\left({x}\right)\:{if}\:{p}\leqslant{x}+\mathrm{1}\:{and}\:{p}\in{Z}\:. \\ $$