MathDB

3

Part of 2007 Canada National Olympiad

Problems(1)

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

Source: Canada 2007

8/1/2007
Suppose that f f is a real-valued function for which f(xy)+f(y−x)≥f(y+x) f(xy)+f(y-x)\geq f(y+x) for all real numbers x x and y y. a) Give a non-constant polynomial that satisfies the condition. b) Prove that f(x)≥0 f(x)\geq 0 for all real x x.
functionalgebrapolynomialfunctional inequalities