Bijection/Examples/Real Cube Function

Example of Bijection

Let $f: \R \to \R$ be the mapping defined on the set of real numbers as:

$\forall x \in \R: \map f x = x^3$

Then $f$ is a bijection.


Proof

A direct application of Integer Power Function is Bijective iff Index is Odd.

$\blacksquare$


Sources

  • 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Composition of Functions
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