Question 56
Find all functions $f : \mathbb{R} \to (0, \infty)$, such that
$$
2^{-x-y} \le \frac{f(x)f(y)}{(x^2+1)(y^2+1)} \le \frac{f(x+y)}{(x+y)^2+1},
$$
for all $x, y \in \mathbb{R}$.
$$
2^{-x-y} \le \frac{f(x)f(y)}{(x^2+1)(y^2+1)} \le \frac{f(x+y)}{(x+y)^2+1},
$$
for all $x, y \in \mathbb{R}$.