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(1 - x^2) f(\frac{2x}{1 + x^2} ) = (1 + x^2)^2 f(x)

Source: 39-th Vietnamese Mathematical Olympiad 2001

March 19, 2007
functionintegrationalgebra proposedalgebra

Problem Statement

Find all real-valued continuous functions defined on the interval (−1,1)(-1, 1) such that (1−x2)f(2x1+x2)=(1+x2)2f(x)(1-x^{2}) f(\frac{2x}{1+x^{2}}) = (1+x^{2})^{2}f(x) for all xx.
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