Replicative Function of x minus Floor of x is Replicative

Theorem
Let $f: \R \to \R$ be a real function.

Let $f$ be a replicative function.

Let $g: \R \to \R$ be the real function defined as:
 * $\map g x = \map f {x - \floor x}$

Then $g$ is also a replicative function.