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China Mathematical Olympiad 1994 problem3

Source: China Mathematical Olympiad 1994 problem3

September 17, 2013
functioninequalitiesalgebra unsolvedalgebra

Problem Statement

Find all functions f:[1,∞)→[1,∞)f:[1,\infty )\rightarrow [1,\infty) satisfying the following conditions: (1) f(x)≤2(x+1)f(x)\le 2(x+1); (2) f(x+1)=1x[(f(x))2−1]f(x+1)=\dfrac{1}{x}[(f(x))^2-1] .
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