1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Proving a fixed point on a function

  1. Oct 2, 2006 #1
    Hello guys, this question is kinda bothering me since I'm having trouble with one of the steps in proving it.

    The question reads. Assume funciton f is continuous on an interval [0,1], such that the range of f is contained within or equal to [0,1]. Show that for a value of c contained within [0,1] there exists f(c)=c.

    I know that the proof process must involve the use of Intermediate Value Theorem, but I can't seem to find a way to show that
    k = c, (k is a arbitrary number contained within [0,1].

    Any tips /help would be appreciated:biggrin:
    Last edited: Oct 2, 2006
  2. jcsd
  3. Oct 2, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    That can't possibly be what your question says. Doesn't it say "show that there exists some c in [0,1] such that f(c)=c"? Consider the function g(x) = x-f(x) and apply IVT.
  4. Oct 3, 2006 #3
    Thank you AKG, problem solved ^^

    I had a similar idea but both worked out ok.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook