How to prove $f:Z \to E$, given by $f(x) = 2x$ is bijective?

Question

I know I must prove that $f$ is both injective and surjective. I've got the injective proof down. But I'm stuck on the surjective proof.

So far I have, for some $x,y ∈ Z$, $y = 2x \Rightarrow x = y/2$. Now does this prove that $f$ is surjective as well since $y$ would also $\in E$ (even numbers)? Or am I missing something?