jmc

Setting $x=4,$ we get $$3f(4)-2f\left(\frac{1}{4}\right)=4.$$Setting $x=\frac{1}{4},$ we get $$3f\left(\frac{1}{4}\right)-2f(4)=\frac{1}{4}.$$We can view these equations as a system in $f(4)$ and $f\left(\frac{1}{4}\right).$ Solving this system, we find $f(4)=\boxed{\frac{5}{2}}.$