MathDB
One variable function in Turkey JBMO TST

Source: Turkey JBMO TST 2023 Day 1 P3

April 30, 2023
functionalgebra

Problem Statement

Find all f:RRf: \mathbb{R} \rightarrow \mathbb{R} such that f(x+f(x))=f(x)f(x+f(x))=f(-x) and for all xyx \leq y it satisfies f(x)  f(y)f(x) \leq f(y)