Let f:R $\to$ R be defined by f(x)=|x-2n| for x $ϵ$ [2n-1,2n+1], n $ϵ$ Z. Then f is periodic with period ___

Q. For every integer $n,$ let $a_n$ and $b_n$ be real numbers. Let function $f:R\to R$ be given by
$f\left(x\right)=\{\begin{array}{c}{a}_n+\sin \pi x,\text{for}x\in [2n,2n+1]\\ b_n+\cos \pi x,\text{for}x\in (2n-1,2n)\end{array}$ , for all integers $n.$
If $f$ is continuous, then which of the following hold(s) for all $n?$

Q. Let $f:R\to R$ be defined by $f\left(x\right)=\frac{1}{x}\forall x\in R$, then $f$ is _____

Q. For every integer $n$, let $a_n$ and $b_n$ be real numbers. Let function $f:IR\to IR$ be given by
$f\left(x\right)=\{\begin{array}{c}{a}_n+\sin \pi x,forx\in [2n,2n+1]\\ b_n+\cos \pi x,forx\in (2n-1,2n)\end{array}$$,forallintegersn.$
lf $f$ is continuous, then which of the following hold(s) for all $n$?

Q. Define a function $f:R\to R$ by $f\left(x\right)=max\{|x|,|x-1|,....|x-2n|\}$
Where $n$ is a fixed natural number, Then ${\int }_0^{2n}f\left(x\right)dx$ is.

Q. Let $f:R\to R$ is defined by $f\left(x\right)=\frac{|x|-1}{|x|+1}$ then $f$ is :