MathDB

Ascendant Function - Iran NMO 2004 (Second Round) - Problem2

Source:

September 24, 2010

functionalgebra proposedalgebra

Problem Statement

Let

f:\mathbb{R}^{\geq 0}\to\mathbb{R}

be a function such that

f(x)-3x

and

f(x)-x^3

are ascendant functions. Prove that

f(x)-x^2-x

is an ascendant function, too. (We call the function

g(x)

ascendant, when for every

x\leq{y}

we have

g(x)\leq{g(y)}