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Thread: How to simplify 1-(1/1+exp(x))

  1. #1
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    Question How to simplify 1-(1/1+exp(x))

    How to simplify the term
    $$1 - \frac{1}{1+\exp(1/x)}$$
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  2. #2
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    Re: How to simplify 1-(1/1+exp(x))

    The only "simplifying" I see is to write "1" as a fraction with denominator 1+ exp(1/x) and do the subtraction.
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  3. #3
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    Re: How to simplify 1-(1/1+exp(x))

    You mean

    $$\frac{1+\exp(1/x) - 1}{1+\exp(1/x)}=\frac{\exp(1/x)}{1+\exp(1/x)}$$

    doesn't it simplify to the sigmoid function?
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  4. #4
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    Re: How to simplify 1-(1/1+exp(x))

    Quote Originally Posted by brianx View Post
    You mean

    $$\frac{1+\exp(1/x) - 1}{1+\exp(1/x)}=\frac{\exp(1/x)}{1+\exp(1/x)}$$

    doesn't it simplify to the sigmoid function?
    No. The sigmoid function deals with $\displaystyle e^{-x} = \frac{1}{e^x}$. This one deals with $\displaystyle e^{1/x}$ which is not the same thing.

    -Dan
    Last edited by topsquark; Apr 17th 2018 at 06:35 AM.
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