MathDB

Let

F:\mathbb R^{\mathbb R}\to\mathbb R^{\mathbb R}

be a function (from the set of real-valued functions to itself) such that

F(F(f)\circ g+g)=f\circ F(g)+F(F(F(g)))

for all

f,g:\mathbb R\to\mathbb R

. Prove that there exists a function

\sigma:\mathbb R\to\mathbb R

such that

F(f)=\sigma\circ f\circ\sigma

for all

f:\mathbb R\to\mathbb R

Problem Statement