Question 92
Find all functions $f:\mathbb R\to\mathbb R$ satisfying:
(1) $f(1+xy)-f(x+y)=f(x)f(y)$ for every $x,y\in\mathbb R$;
(2) $f(-1)\ne0$.
(1) $f(1+xy)-f(x+y)=f(x)f(y)$ for every $x,y\in\mathbb R$;
(2) $f(-1)\ne0$.
MathNet 2013 Question 92
Math Olympiad Vault · MathNet 2013