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Math Help - Determine if the function is a contraction! Thank you!

  1. #1
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    Determine if the function is a contraction! Thank you!

    The function is g(x) = (1/2)*(e^(-x)) x is R

    Thank you!!!!
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  2. #2
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    Re: Determine if the function is a contraction! Thank you!

    Use the mean value theorem.
    Last edited by emakarov; February 2nd 2013 at 11:17 AM.
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  3. #3
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    Re: Determine if the function is a contraction! Thank you!

    What happens as x goes to -\infty? For it to be a contraction, |g'(x)| has to be less than 1, right?

    - Hollywood
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  4. #4
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    Re: Determine if the function is a contraction! Thank you!

    Actually, there are several different ways to define "contraction". jack56890, what definition are you using?
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  5. #5
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    Re: Determine if the function is a contraction! Thank you!

    My definition is that a function is a contraction if there is a real number c, 0\le{c}<1 such that |g(x)-g(y)|\le{c}|x-y| for all x,y\in\mathbb{R} where g(x) and g(y) are defined. Just so that you can put my post in context - if you're using a different definition, my post might not make sense.

    - Hollywood
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