E:14336

S:E14336 (Gh. Szöllösy)

Fie $a$ și Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} două numere reale nenule, fixate. Deteriminați toate funcțiile Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f : \mathbb{R} \to \mathbb{R}} cu proprietatea: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)-f(y)=(ax + by)f(x)f(y),}
pentru orice $x$ și $y$ numere reale.

Soluție.