Find the function!

I've been seriously busy so I haven't had time something "interesting"... however, let me share this problem I found in the board of the kitchen:

Find all functions $f:\mathbb Q_+\rightarrow\mathbb R$ such that:
1. $f(x+y)\geq f(x)+f(y)$.
2. $f(xy)\leq f(x)f(y)$.
3. $\exists a>1$ such that $f(a)=a$.

If you find them... I guess your having more free time than I do. Good luck!