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Find all functions (something like tangents) - [ILL 1971]

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January 11, 2011
functionalgebrafunctional equationalgebra proposed

Problem Statement

Determine all real functions f(x)f(x) that are defined and continuous on the interval (−1,1)(-1, 1) and that satisfy the functional equation f(x+y)=f(x)+f(y)1−f(x)f(y)(x,y,x+y∈(−1,1)).f(x+y)=\frac{f(x)+f(y)}{1-f(x) f(y)} \qquad (x, y, x + y \in (-1, 1)).
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