Question 13
Find all the functions $f$ defined in the set of nonnegative real numbers and that take nonnegative real values, such that 1) $\quad f(x f(y)) f(y)=f(x+y)$ for all $x, y \geq 0$, 2) $\quad f(2)=0$, 3) $\quad f(x) \neq 0$ for $0 \leq x\lt 2$.