Surjection/Examples/Doubling Function on Reals

Example of Surjection
Let $f: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map f x = 2 x$

Then $f$ is a surjection.

Proof
For $f$ to be a surjection, it is necessary that:
 * $\forall y \in \R: \exists x \in \R: y = 2 x$

This is the case.

Thus $f$ is a surjection by definition.