Question Number 30563 by abdo imad last updated on 23/Feb/18
![let f(x)=∣x−2 [((x+1)/2)]∣ 1) prove that f is periodic 2) simplify f(x) if p≤x+1 and p∈Z .](https://www.tinkutara.com/question/Q30563.png)
$${let}\:{f}\left({x}\right)=\mid{x}−\mathrm{2}\:\left[\frac{{x}+\mathrm{1}}{\mathrm{2}}\right]\mid \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\:{is}\:{periodic} \\ $$$$\left.\mathrm{2}\right)\:{simplify}\:{f}\left({x}\right)\:{if}\:{p}\leqslant{x}+\mathrm{1}\:{and}\:{p}\in{Z}\:. \\ $$