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:
 * $g \left({x}\right) = f \left({x - \left \lfloor{x}\right \rfloor}\right)$

Then $g$ is also a replicative function.