MathDB

Continuous Function on Open Interval

Source: Romanian District Olympiad 2018 - Grade XI - Problem 4

March 10, 2018

functioncontinuityreal analysis

Problem Statement

Let

a < b

be real numbers and let

f : (a, b) \to \mathbb{R}

be a function such that the functions

g : (a, b) \to \mathbb{R}

g(x) = (x - a) f(x)

and

h : (a, b) \to \mathbb{R}

h(x) = (x - b) f(x)

are increasing. Show that the function

f

is continuous on

(a, b)