jmc

Setting $x=2,$ we get $$f(2)-2f\left(\frac{1}{2}\right)=16.$$Setting $x=1/2,$ we get $$f\left(\frac{1}{2}\right)-2f(2)=2.$$Solving these equations as a system in $f(2)$ and $f\left(\frac{1}{2}\right),$ we obtain $f(2)=\boxed{-\frac{20}{3}}$ and $f\left(\frac{1}{2}\right)=-\frac{34}{3}.$