Question 178
Find all possible values of $f(2018)$ where $f$ is a function from $\mathbb{Q}$ to $\mathbb{R}_{+}$ satisfying the following three conditions:
- $f(2)=1 / 2$ ;
- for every rational $x$, if $f(x) \leqslant 1$, then $f(x+1) \leqslant 1$;
- $f(x y)=f(x) f(y)$ for all rationals $x$ and $y$.
- $f(2)=1 / 2$ ;
- for every rational $x$, if $f(x) \leqslant 1$, then $f(x+1) \leqslant 1$;
- $f(x y)=f(x) f(y)$ for all rationals $x$ and $y$.