Injection/Examples/Cube Function

Example of Injection
Let $f: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map f x = x^3$

Then $f$ is an injection.

Proof
From Odd Power Function on Real Numbers is Strictly Increasing, $f$ is strictly increasing.

From Strictly Monotone Real Function is Bijective, it follows that $f$ is bijective.

Hence by definition $f$ is an injection.