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function f(x)

Source: China south east mathematical Olympiad 2007 problem 5

July 12, 2013

functioninequalitiesalgebra unsolvedalgebra

Problem Statement

Let

f(x)

be a function satisfying

f(x+1)-f(x)=2x+1 (x \in \mathbb{R})

.In addition,

|f(x)|\le 1

holds for

x\in [0,1]

. Prove that

|f(x)|\le 2+x^2

holds for

x \in \mathbb{R}