Constant Multiple of Replicative Function is Replicative

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

Let $f$ be a replicative function.

Let $c \in \R$ be a constant.

Let $g: \R \to \R$ be the real function defined as:
 * $\map g x = c \map f x$

Then $g$ is also a replicative function.

Proof
Hence the result by definition of replicative function.