Extension of Mapping/Examples/Extension of Square Function on Natural Numbers

Example of Extension of Mapping
Let $f: \N \to \N$ be the mapping defined as:
 * $\forall n \in \N: \map f n = n^2$

Let $h: \R \to \R$ be the mapping defined as:
 * $\forall x \in \R: \map h x = x^2$

Then $h$ is a extension of $f$.