Question Number 140587 by mathsuji last updated on 09/May/21
$${a};{b}>\mathrm{0}\:{and}\:\forall{x};{y}\in\mathbb{R} \\ $$ $${find}\:{all}\:{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:;\:{such}\:{that} \\ $$ $${f}\left({ax}\right){f}\left({by}\right)={abf}\left({bx}+{ay}\right)+{x}^{{a}} {y}^{{b}} {f}\left({x}^{{b}} {y}^{{a}} \right) \\ $$