Exactly two functions

Show that there exist exactly two functions $f : \Bbb Q → \Bbb Q$ with the property

$f(x + y) = f(x) + f(y)$ and $f(x · y) = f(x) · f(y)$
for all $x, y \in \Bbb Q$.

I am unsure how to prove that there are no more than two functions that meet the requirements. I can come up with an example $f(x) = x$ which obviously satisfy the constraints but I can't see a way to prove that there are only two functions.