$f(x)$ is a polynomial which satisfies $f(x)f(\frac 1 x)+5-3f(x)-3f(\frac 1 x)=0$ for all $x\in \mathbb R-\{0\}$. If $f(2)=11$, find f(3).
I simplified the functional equation down to $g(x)g(\frac 1 x)=4$, where $g(x)=f(x)-3$. I was able to get correct answer by assuming $f(x)$ to be a quadratic polynomial and putting values of $f(2)$ and $f(1/2)$, but I would appreciate a proper solution of this functional equation, specifically in solving $g(x)g(\frac 1x)=4$.