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Continuous function solutions

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that a continuous function such that for all c in the reals, the equation f(x) = c cannot have two solutions

    2. Relevant equations



    3. The attempt at a solution

    I was thinking along the lines of a contradiction or somehow using intermediate value theorem but it seems like it is so easy it is hard.
     
  2. jcsd
  3. Nov 12, 2008 #2

    Office_Shredder

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    What are you actually trying to prove here? Your sentence doesn't parse properly
     
  4. Nov 12, 2008 #3
    show that a continuous function cannot have two solutions for the equation f(x) = c for every c.
     
  5. Nov 12, 2008 #4

    Office_Shredder

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    I have f(x) = c... am I solving for x given c? What you're trying to say is that f can't be two to one (i.e. for every point p in the image, there are two points in the preimage of p).

    Contradiction is a good place to start. There have to be two points that f maps to zero, consider f on the interval between them
     
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