MathDB
Continuous f(x-f(x))=x/2 does not exist

Source: Turkey TST 2001 - P6

April 4, 2013
functionalgebra proposedalgebra

Problem Statement

Show that there is no continuous function f:RRf:\mathbb{R}\rightarrow \mathbb{R} such that for every real number xx f(xf(x))=x2.f(x-f(x)) = \dfrac x2.