Nested fractional function equation
Source: AIMO 2007, TST 5, P2
January 11, 2009
functionalgebrafunctional equationalgebra unsolved
Problem Statement
Determine all functions f: \mathbb{R}^\plus{} \mapsto \mathbb{R}^\plus{} which satisfy f \left(\frac {f(x)}{yf(x) \plus{} 1}\right) \equal{} \frac {x}{xf(y)\plus{}1} \forall x,y > 0