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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


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    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.
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