MathDB

1

Part of 2008 Iran Team Selection Test

Problems(1)

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

Source: Iran TST 2008

5/20/2008
Find all functions f:R⟶R f: \mathbb R\longrightarrow \mathbb R such that for each x,y∈R x,y\in\mathbb R: f(xf(y)) \plus{} y \plus{} f(x) \equal{} f(x \plus{} f(y)) \plus{} yf(x)