jmc

Setting $x=-2,$ we get $$3f\left(-\frac{1}{2}\right)-f(-2)=4.$$Setting $x=-\frac{1}{2},$ we get $$3f(-2)-4f\left(-\frac{1}{2}\right)=\frac{1}{4}.$$Solving these equations as a system in $f(-2)$ and $f\left(-\frac{1}{2}\right),$ we find $f(-2)=\boxed{\frac{67}{20}}$ and $f\left(-\frac{1}{2}\right)=\frac{49}{20}.$