Let $f(x)=|1-2 x|$, then

A function $f: \mathbb{R} \rightarrow \mathbb{R}$, satisfies $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)+f(0)}{3}$ for all $x, y \in \mathbb{R}$. If the function ' $f$ ' is differentiable at $x=0$, then $f$ is

The set of points of discontinuity of the function $f(x)=x-[x], x \in \mathbb{R}$ is