MathDB

5

Part of 2017 OMMock - Mexico National Olympiad Mock Exam

Problems(1)

Determine functions for fixed k

Source: Mexico National Olympiad Mock Exam 2017 P5

11/4/2019
Let kk be a positive real number. Determine all functions f:[−k,k]→[0,k]f:[-k, k]\rightarrow[0, k] satisfying the equation f(x)2+f(y)2−2xy=k2+f(x+y)2f(x)^2+f(y)^2-2xy=k^2+f(x+y)^2 for any x,y∈[−k,k]x, y\in[-k, k] such that x+y∈[−k,k]x+y\in[-k, k].
Proposed by Maximiliano Sánchez
algebrafunctional equationfunction