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

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

Let $S = \set {x \in \N: \exists y \in \N_{>0}: x = 2 y} = \set {2, 4, 6, 8, \ldots}$

Let $g: S \to \N$ be the mapping defined as:
 * $\forall n \in \N: \map g n = n^2$

Then $g$ is a restriction of $f$.