Periodicity of $f$ such that $ f(x+2)=f(x-1)f(x+5)$

Question

Let $f$ be a real valued function defined from :$\mathbb{R}\to \mathbb{R^*}$ such that

$$ f(x+2)=f(x-1)f(x+5).$$

How do i show that $f$ is peridoic ?

Note: I have tried to show that for every real number $x$ that $f(x+2)=f(x)$ but I can't since I ignored the form of the function

Answer 1

Hint:   $f(x)=f(x-3)f(x+3)=f(x-6)f(x)f(x+3) \implies f(x-6)f(x+3)=1\,$.