MathDB

1

Part of 2010 Middle European Mathematical Olympiad

Problems(1)

Find all functions f with f(x+y)+f(x)f(y)=f(xy)+(y+1)f(x)+(x+1)f(y)

Source: (4th Middle European Mathematical Olympiad, Individual Competition, Problem 1)

9/11/2010
Find all functions f:R→Rf:\mathbb{R}\to\mathbb{R} such that for all x,y∈Rx, y\in\mathbb{R}, we have f(x+y)+f(x)f(y)=f(xy)+(y+1)f(x)+(x+1)f(y).f(x+y)+f(x)f(y)=f(xy)+(y+1)f(x)+(x+1)f(y).
functionalgebrafunctional equationalgebra solved