Functional equation: f(y·f(x))·f(x) = f(x+y)
Source: German DEMO 2008, grade 11-13, round 4, problem 3
May 22, 2008
functionalgebra proposedalgebra
Problem Statement
Find all functions defined on non-negative real numbers having the following properties:
(i) For all non-negative it is .
(ii) It is f\left(1\right)\equal{}\frac 12.
(iii) For all non-negative numbers it is f\left( y \cdot f(x) \right) \cdot f(x) \equal{} f(x\plus{}y).