MathDB
f(f(f(x)))=x ; ISI BS 2011, P3

Source:

March 31, 2013
function

Problem Statement

Let R\mathbb{R} denote the set of real numbers. Suppose a function f:R→Rf: \mathbb{R} \to \mathbb{R} satisfies f(f(f(x)))=xf(f(f(x)))=x for all x∈Rx\in \mathbb{R}. Show that
(i) ff is one-one,
(ii) ff cannot be strictly decreasing, and
(iii) if ff is strictly increasing, then f(x)=xf(x)=x for all x∈Rx \in \mathbb{R}.
Back to ProblemsView on AoPS