This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2014 Contests, 1
Tags: function , algebra , functional equation , fe , memo , memo 2014 , Reals
Determine all functions $f:\mathbb{R} \to \mathbb{R}$ such that \[ xf(y) + f(xf(y)) - xf(f(y)) - f(xy) = 2x + f(y) - f(x+y)\] holds for all $x,y \in \mathbb{R}$.

2014 Middle European Mathematical Olympiad, 1
Tags: function , algebra , functional equation , fe , memo , memo 2014 , Reals
Determine all functions $f:\mathbb{R} \to \mathbb{R}$ such that \[ xf(y) + f(xf(y)) - xf(f(y)) - f(xy) = 2x + f(y) - f(x+y)\] holds for all $x,y \in \mathbb{R}$.