Function notation for specifying (co)domain and mapping at once

Question

I am looking for conventions of spelling out a function type together with a mapping. I have found some possibilities:

1. using intermediate words: $$f \colon R \to R\ \text{where}\ x \mapsto x^2$$
2. writing stuff above each other: $$\begin{align}f \colon &R \to R \\ &x \mapsto x^2\end{align}$$
3. putting another colon in between: $$f \colon R \to R : x \mapsto x^2$$

There are also various possibilities to write the mapping part

• $f \colon x \mapsto x^2$
• $f(x) = x^2$
• $\lambda(x).x^2$

Is there a prevalent way of writing both parts of the definition?