The function \(f : \mathbb{R} \to \mathbb{R}\) satisfies
\(f(x) f(y) = f(x + y) + xy\)
for real numbers \(x\) and \(y\).. Find all possible functions \(f\).
I've found that \(f(0)=1\) and if \(f(-1)\) is not \(0,\) then \(f(1)=0.\) I'm just stuck and any answer/help would be appreciated! (btw i got the values for \(f(0)\) and \(f(1)\) by plugging in values for x and y like 0 and 0, or x=1, y=1.)
------------Thanks!