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Sigmoid function

  1. Jan 15, 2012 #1
    Hi,
    I'm working with the sigmoid function which is written

    1/(1 + e^-t)

    While plugging this in to wolfram alpha, I noticed an alternate way to write it is

    1 - 1/(1 + e^t)

    I can't for the life of me figure out how to go about rewriting it in the alternate form. Would anyone be able to give me a hint on how to go about rewriting it this way? Or even better point me at some material that will help me figure it out? Thanks

    Here is the link to wolfram alpha

    http://www.wolframalpha.com/input/?i=1/(1+++exp(-t))
     
  2. jcsd
  3. Jan 15, 2012 #2

    AlephZero

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    Start by multipling the top and bottom of 1/(1 + e^-t) by e^t.
     
  4. Jan 15, 2012 #3

    epenguin

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    1/(1 + e-t) = 1/(1 + 1/et) = et/(1 + et) = (1 + et -1)/(1 + et) =

    you can complete.

    Nothing difficult, only thing difficult to understand maybe is why they want it in that form.
     
  5. Jan 15, 2012 #4
    Thanks guys. That helped. So to complete would you end up with

    1/(1 + et) + 1et/(1 + et) - 1/(1 + et) = 1 - 1/(1 + et)
     
    Last edited: Jan 15, 2012
  6. Jan 15, 2012 #5

    AlephZero

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    It shows the function is "symmetrical" in the sense that f(t) + f(-t) = 1, which isn't obvious from either expression on its own.
     
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