Beautiful Symmetric Rational Function

Algebra Level 3

f(x)=(x1)(x2)(x3)(x4)(x3)(x2)(x1)(x2)(x4)(x2) f(x) = \dfrac{(x-1)(x-2)(x-3)(x-4)(x-3)(x-2)(x-1)}{(x-2)(x-4)(x-2)}

How many values of x x satisfy the equation f(x)=1 f(x) = 1 ?

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