Question 67
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function that satisfies the functional equation
$$
f(x-y)=2009 f(x) f(y)
$$
for all $x, y \in \mathbb{R}$. If $f(x)$ is never zero, what is $f(\sqrt{2009})$?
$$
f(x-y)=2009 f(x) f(y)
$$
for all $x, y \in \mathbb{R}$. If $f(x)$ is never zero, what is $f(\sqrt{2009})$?