Let $f:\mathbb{R} \rightarrow\mathbb{R}$ defined by $f(x)=x^2$.
Let's, for instance, say that we want to know the deriviative of function $f$ at $x=2$, which is the limit of the function $g(h)=\dfrac{f(2+h)-f(2)}{h}$ as $h$ approches $0$.
I would like to know: formally - and in general, not only in the example of $f(x)=x^2$ - what is the domain and codomain of the function $g$?
Thanks.