finding functions $f, g$ so $g(f(x)) = x + 4$

Question

I'm trying to find an example for functions $f,g: \mathbb{N} \to \mathbb{N}$, so that $g(f(x)) = x + 4$, where $f$ is not surjective and $g$ is neither surjective nor injective.

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I thought about $f(x) = x + 1$ and $g(x) = x + 3$ but then $g$ is injective...

Answer 1

Let $f(x)=x+4$ and $g(x)=x $ for any $x\geq5$ and $g(x)=1$ for $x<5$.