Functional Equation Fun

Algebra Level 5

\[ f(x)+f\left(\frac{6x-5}{4x-2}\right)=x\]

Find the number of real-valued functions \(f,\) that are solutions of the above functional equation, and whose domain is the set of all real numbers different from \(\frac{1}{2}\), \(1\), and \(\frac{3}{2}\).