continuous function

let f: R->R be a continuous function such that f(0)=f(2)=1. then there exists c>0 such that f(c)=c
prove this. 


Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
Erdos Erdos
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.