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Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation

F(x) + F((2x - 3)/x) = x.

Find the function F(x) satisfying these conditions.  Write F(x) as a rational function with expanded polynomials in the numerator and denominator.

 Nov 7, 2022
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F(x) = (-x^3 + 2x)/(x^2 + 2)

 Nov 7, 2022

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