I am trying to find a function that suits my needs for an AI project that I am working on the specifications are below. If you know any function that fits that description please let me know or if not you could get me started on how to look for such a specific function and if it even exists (I am very much a noob when it comes to these things so I apologies for the idiotic nature of my questioning)
Description
it needs to be infinite that is for every y there needs to be an x corresponding to it (like f(x)=x) both negative and positive, It needs to be nonlinear and it has to have a positive derivitive and also a inverse
Do any of you know of such a function?
You could try $x^3+x$ or $e^x-e^{-x}$.