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f(x - y + z) = f(x) + f(y) + f(z) - xy - yz + xz

Source: Switzerland - 2009 Swiss MO Final Round p6

December 26, 2022
algebrafunctionalfunctional equation

Problem Statement

Find all functions f:R>0→R>0f : R_{>0} \to R_{>0}, which for all x>y>z>0x > y > z > 0 is the following equation holds f(x−y+z)=f(x)+f(y)+f(z)−xy−yz+xz.f(x - y + z) = f(x) + f(y) + f(z) - xy - yz + xz.
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