Find all functions $f\colon\mathbb R^+\to\mathbb R^+$ such that \[(f(x)+f(y)+f(z))(xf(y)+yf(z)+zf(x))>(f(x)+y)(f(y)+z)(f(z)+x)\]for all $x,y,z\in\mathbb R^+$. Alexander Wang (oops)
Source: Revenge ELMO 2023/3
Tags: algebra, revenge elmo
Find all functions $f\colon\mathbb R^+\to\mathbb R^+$ such that \[(f(x)+f(y)+f(z))(xf(y)+yf(z)+zf(x))>(f(x)+y)(f(y)+z)(f(z)+x)\]for all $x,y,z\in\mathbb R^+$. Alexander Wang (oops)