What is the name of this function $f(x) = \frac{1}{1+x^n}$?

Question

$f(x\in\mathbb{R}) = \frac{1}{1+x^n}$

Answer 1

This function $f$ can be pronounced phonetically as "One over the sum of one and $x$ to the $n$th power".

Answer 2

In the particular case where $n$ is even, this looks like the pdf of the Cauchy distribution, so you might want to say that $f(x) = \frac{1}{1+x^{2n}}$ is some kind of a generalized Cauchy...

Answer 3

Not every function deserves a name beyond the one it defines for itself by merely describing it (like in Ethan's answer).

EDIT: I would emphasise the spacing to avoid ambiguity:

One over $\quad$ one plus $\quad x$ to the $n$th power.