Question 84
Find all functions $f: \mathbb{R}_{\gt 0} \rightarrow \mathbb{R}_{\gt 0}$ which satisfy the following equation for all $x \gt y \gt z \gt 0$:
$$
f(x-y+z)=f(x)+f(y)+f(z)-x y-y z+x z
$$
$$
f(x-y+z)=f(x)+f(y)+f(z)-x y-y z+x z
$$
MathNet 2009-part-04 — 175 problems (EN–VI) Question 84
Math Olympiad Vault · MathNet 2009-part-04 — 175 problems (EN–VI)