MathDB

Possible limits of a function with a certain equation

Source: VJIMC 2018, Category I, Problem 4

April 14, 2018

functionfunctional equationDecreasinglimit

Problem Statement

Determine all possible (finite or infinite) values of

\lim_{x \to -\infty} f(x)-\lim_{x \to \infty} f(x),

f:\mathbb{R} \to \mathbb{R}

is a strictly decreasing continuous function satisfying

f(f(x))^4-f(f(x))+f(x)=1

for all

x \in \mathbb{R}