MathDB

Function doesn't exist when power of y is > 1

Source: Italy TST 1999

February 1, 2011

functionalgebra proposedalgebra

Problem Statement

(a) Find all strictly monotone functions

f:\mathbb{R}\rightarrow\mathbb{R}

such that f(x+f(y))=f(x)+y \text{for all real}\ x,y. (b) If

n>1

is an integer, prove that there is no strictly monotone function

f:\mathbb{R}\rightarrow\mathbb{R}

such that f(x+f(y))=f(x)+y^n \text{for all real}\ x, y.