MathDB

Determine all functions

f:\mathbb{R}\to\mathbb{R}

, where

\mathbb{R}

is the set of all real numbers, satisfying the following two conditions: 1) There exists a real number

M

such that for every real number

x,f(x)<M

is satisfied. 2) For every pair of real numbers

x

and

y

f(xf(y))+yf(x)=xf(y)+f(xy)

is satisfied.

Problem Statement