MathDB

1

Part of 2008 Pan African

Problems(2)

f(x+y) is at most f(x)+f(y), which is at most x+y

Source: Pan African Olympiad 2008

10/1/2011
Determine all functions f:R→Rf:\mathbb{R}\to\mathbb{R} satisfying f(x+y)≤f(x)+f(y)≤x+yf(x+y)\le f(x)+f(y)\le x+y for all x,y∈Rx,y\in\mathbb{R}.
functionalgebra proposedalgebra
Too easy to be in a mathematical competition surely...

Source: Pan African Olympiad 2008

10/1/2011
Let xx and yy be two positive reals. Prove that xy≤xn+2+yn+2xn+ynxy\le\frac{x^{n+2}+y^{n+2}}{x^n+y^n} for all non-negative integers nn.
inequalitiesrearrangement inequalityinequalities proposed