MD-MO 2008 Problem 2

Find $f(x): (0,+\infty) \to \mathbb R$ such that $$f(x)\cdot f(y) + f(\frac{2008}{x})\cdot f(\frac{2008}{y})=2f(x\cdot y)$$ and $f(2008)=1$ for $\forall x \in (0,+\infty)$ .