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Functional equation with abcd=1 - Switzerland 2011

Source:

March 22, 2011
functionalgebra proposedalgebra

Problem Statement

Find all functions f:R+ā†’R+f:\mathbb{R}^+\to\mathbb{R}^+ such that for any real numbers a,b,c,d>0a, b, c, d >0 satisfying abcd=1abcd=1,(f(a)+f(b))(f(c)+f(d))=(a+b)(c+d)(f(a)+f(b))(f(c)+f(d))=(a+b)(c+d) holds true.
(Swiss Mathematical Olympiad 2011, Final round, problem 4)
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