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Linear function

Source: China TST 2009, Quiz 2, Problem 3

March 21, 2009
functionalgebra proposedalgebra

Problem Statement

Consider function f:Rā†’R f: R\to R which satisfies the conditions for any mutually distinct real numbers a,b,c,d a,b,c,d satisfying \frac {a \minus{} b}{b \minus{} c} \plus{} \frac {a \minus{} d}{d \minus{} c} \equal{} 0, f(a),f(b),f(c),f(d) f(a),f(b),f(c),f(d) are mutully different and \frac {f(a) \minus{} f(b)}{f(b) \minus{} f(c)} \plus{} \frac {f(a) \minus{} f(d)}{f(d) \minus{} f(c)} \equal{} 0. Prove that function f f is linear
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