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Give a polynomial example for f if f(xy)+f(y-x)\geq f(y+x)

Source: Canada 2007

August 1, 2007

functionalgebrapolynomialfunctional inequalities

Problem Statement

Suppose that

f

is a real-valued function for which

f(xy)+f(y-x)\geq f(y+x)

for all real numbers

x

and

y

. a) Give a non-constant polynomial that satisfies the condition. b) Prove that

f(x)\geq 0

for all real

x