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

Source: 10th QEDMO p1 Juniors (8-10. 12. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 16, 2021
algebrafunctional equationfunctional

Problem Statement

Find all functions f:R→Rf: R\to R with the property that xf(y)+yf(x)=(x+y)f(xy)xf (y) + yf (x) = (x + y) f (xy) for all x,y∈Rx, y \in R.
Back to ProblemsView on AoPS