$ \frac{1}{e^x+1} $ and $ \frac{e^x}{e^x+1} $
Just wonder if either of the above function has a term/name associated with it? Or they are just functions that look beautiful without names? Maybe they appear very often under certain contexts?
I thought I might have seen it in some online courses. Maybe it was graphical model related or something else. But I'm not exactly sure right now and I cannot really find it on Google.
Hint
Quotic Wikipedia article :"A logistic function or logistic curve is a common special case of the more general sigmoid function, with equation $$f(x)=\frac{1}{1+e^{-x}}$$ So, multiplying numerator and denominator by $e^x$ $$f(x)=\frac{e^x}{1+e^{x}}$$ is just the same and $$g(x)=\frac{1}{1+e^{x}}=1-f(x)$$