Problem 1050

Certainly 0,2 are fixed points of $f$ and therefore solutions. On the other hand, there can be no solutions for $x<0$, since $f$ is nonnegative-valued; for $0<x<2$, we have $0 \leq f(x)<x<2$ (and $f(0)=0$ ), so iteration only produces values below $x$, and for $x>2, f(x)>x$, and iteration produces higher values. So there are no other solutions.