Question 113
Let $\mathbb{R}$ denote the set of all real numbers. For each pair $(\alpha, \beta)$ of nonnegative real numbers subject to $\alpha+\beta \geq 2$, determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying
$$
f(x) f(y) \leq f(x y)+\alpha x+\beta y
$$
for all real numbers $x$ and $y$.
$$
f(x) f(y) \leq f(x y)+\alpha x+\beta y
$$
for all real numbers $x$ and $y$.