2013 ToT Fall Senior O p5 f(f(x))=x, g(g(x))=x, f(g(x))>x, g(f(x))>x
Source:
March 22, 2020
functionalgebrainequalities
Problem Statement
Do there exist two integer-valued functions f and g such that for every integer x we have
(a) f(f(x))=x,g(g(x))=x,f(g(x))>x,g(f(x))>x ?
(b) f(f(x))<x,g(g(x))<x,f(g(x))>x,g(f(x))>x ?