RO-NMO 2017 Problem 102

A function $f:\mathbb{Q}_{>0}\longrightarrow\mathbb{Q}$ has the following property: $$f(xy)=f(x)+f(y), x,y\in\mathbb{Q}_{>0}$$ a) Demonstrate that there are no injective functions with this property.b) Do exist surjective functions having this property?