Question 20
Let $\mathbb{R}$ denote the set of all real numbers. Find all functions $f : (0, \infty) \to \mathbb{R}$ satisfying
$$ \left(x + \frac{1}{x}\right) f(y) = f(xy) + f\left(\frac{y}{x}\right), \text{ for all } x, y \gt 0. $$
$$ \left(x + \frac{1}{x}\right) f(y) = f(xy) + f\left(\frac{y}{x}\right), \text{ for all } x, y \gt 0. $$