Say I want a random generator of functions like this:
\begin{align} f: &\mathbb{R} \to \mathbb{R} \\ &x \mapsto f(x) \end{align}
It can be usual functions of course, like $\sin(x)$ or $\exp(x)$ for instance. But what about functions that are not defined and can not be defined from usual functions. Where would you start to build such a generator?
Important precision: here I am asking about all functions, but for my application I'm really only interested in continuous strictly monotonic functions. So if you have an answer for that, I'll already be satisfied.