Real Square Function is neither Injective nor Surjective

Example of Mapping which is Not an Injection nor a Surjection
Let $f: \R \to \R$ be the real square function:
 * $\forall x \in \R: \map f x = x^2$

Then $f$ is neither an injection nor a surjection.

Proof
Consider the real square function:


 * Real-square-function.png

From Real Square Function is not Injective:


 * $f$ is not an injection.

From Real Square Function is not Surjective:


 * $f$ is not a surjection.