I have a function that works like this
f(x) = y
I can run it with whatever x I like, here are a couple of results
f(500) = 3.6
f(250) = 7.2
What I need to do is recreate the function but in order to do that I must first realize how it works. Obviously the input and output are inverse proportional and bound by a factor of 2 but I'm having a hard time describing that mathematically...
Without telling us more about the function, it is impossible to answer your question. There are infinitely many functions which satisfy the conditions $f(500)=3.6$ and $f(250)=7.2$.
For example, one of them would be
$$f(x)=\begin{cases}7.2 & \text{if }x=250\\ 3.6&\text{if } x=500\\ \pi& \text{otherwise}\end{cases}$$
There is nothing about your question that we can use to conclude that the above function isn't what we are looking for, but also nothing to conclude that it is.