Injection/Examples/2x+1 Function on Integers

Example of Injection
Let $f: \Z \to \Z$ be the mapping defined on the set of integers as:
 * $\forall x \in \Z: \map f x = 2 x + 1$

Then $f$ is an injection.

Proof
Let $x_1$ and $x_2$ be integers.

Then:

Hence $f$ is an injection by definition.