MathDB

4

Part of 1999 IMC

Problems(2)

functional equation

Source: IMC 1999 day 1 problem 4

11/19/2005
Find all strictly monotonic functions f:R+→R+f: \mathbb{R}^+\rightarrow\mathbb{R}^+ for which f(x2f(x))=xf\left(\frac{x^2}{f(x)}\right)=x for all xx.
functionreal analysisreal analysis unsolved
there exists none

Source: IMC 1999 day 2 problem 4

11/19/2005
Prove that there's no function f:R+→R+f: \mathbb{R}^+\rightarrow\mathbb{R}^+ such that f(x)2≥f(x+y)(f(x)+y)f(x)^2\ge f(x+y)\left(f(x)+y\right) for all x,y>0x,y>0.
functioninequalitieslimitreal analysisreal analysis unsolved