KURSCHAK 2020 Problem 2

Find all functions $f\colon \mathbb{Q}\to \mathbb{R}_{\geq 0}$ such that for any two rational numbers $x$ and $y$ the following conditions hold

• $f(x+y)\leq f(x)+f(y)$ ,
• $f(xy)=f(x)f(y)$ ,
• $f(2)=1/2$ .