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CR-MO 2013 F2

    Find all functions f:R−{0,2}→Rf:R -\{0,2\} \to R that satisfy for all x≠0,2x \ne 0,2 f(x)⋅(f(2+x2−x3))2=x34f(x) \cdot \left(f\left(\sqrt[3]{\frac{2+x}{2-x}}\right) \right)^2=\frac{x^3}{4}

    Dataset text AI-MO AoPS. Quoted with source.

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