MathDB

Interesting Function

Source: 1983 National High School Mathematics League, Exam Two, Problem 2

February 21, 2020

function

Problem Statement

Function

f(x)

is defined on

[0,1]

f(0)=f(1)

. For any

x_1,x_2\in [0,1], |f(x_1)-f(x_2)|<|x_1-x_2|(x_1\neq x_2)

. Prove that

|f(x_1)-f(x_2)|<\frac{1}{2}