Question 33
Let $f: \mathbb{R} \to \mathbb{R}$ be an arbitrary function and $g: \mathbb{R} \to \mathbb{R}$ be a quadratic function such that: for any reals $m$ and $n$, the equation $f(x) = mx + n$ has solutions if and only if the equation $g(x) = mx + n$ has solutions. Prove $f = g$.
Vasile Pop
Vasile Pop