Functional Equation Fun

Algebra Level 5

f(x)+f(6x54x2)=x f(x)+f\left(\frac{6x-5}{4x-2}\right)=x

Find the number of real-valued functions ff that are solutions of the above functional equation and whose domain is the set of all real numbers different from 12\frac{1}{2}, 11, and 32\frac{3}{2}.

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