Injection/Examples/Cube Function

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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.


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.