Here is the full question. Consider a function $f:\mathbb{Z}\longrightarrow\mathbb{Z}$ such that $f(2n) = n + 3$ for $n\in\mathbb{N}$. Prove that $f$ is not an injective function.
At first I thought I could solve it by replace the n on the right with 2n, so f(n) = (2n) + 3. But that doesn't seem right. I also tried looking for this form of functions, but I don't know what to search for.
I suppose that $f$ is defined on $D=\{2n: n \in \mathbb N\}$
Then we have
$f(2)=f(2 \cdot 1)=1+3=4, \quad f(4)=f(2 \cdot 2)=2+3=5,\quad f(6)=f(2 \cdot 3)=3+3=6,$ etc ....