a-b-gt-0-and-x-y-R-find-all-functions-f-R-R-such-that-f-ax-f-by-abf-bx-ay-x-a-y-b-f-x-b-y-a-

Question Number 140587 by mathsuji last updated on 09/May/21

a; b > 0 a n d \forall x; y \in R

f i n d a l l f u n c t i o n s f : R \to R; s u c h t h a t

f (a x) f (b y) = a b f (b x + a y) + x^{a} y^{b} f (x^{b} y^{a})