MathDB
(f (x) - f (y)) (u - v) = (f (u) - f (v)) (x - y) when x + y = u + v

Source: Ukraine TST 2014 p11

April 30, 2020
functional equationfunctionalalgebra

Problem Statement

Find all functions f:R→Rf: R \to R that satisfy the condition (f(x)−f(y))(u−v)=(f(u)−f(v))(x−y)(f (x) - f (y)) (u - v) = (f (u) - f (v)) (x -y) for arbitrary real x,y,u,vx, y, u, v such that x+y=u+vx + y = u + v.
Back to ProblemsView on AoPS