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

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

How to simplify the term
$$1 - \frac{1}{1+\exp(1/x)}$$

2. 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.

3. 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?

4. Re: How to simplify 1-(1/1+exp(x))

Originally Posted by brianx
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