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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.

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    Domain: the reals $\ne 0$, since you explicitly mentioned the reals. Codomain: Don't know, is that like cosine?2012-05-15
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    The range is $\mathbb{R}\setminus \{4\}$.2012-05-15
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    @AndréNicolas: [Codomain](http://en.wikipedia.org/wiki/Codomain) is a common word for the target of a map. I'm curious as to the term you use for it.2012-05-15
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    @ZevChonoles: Do not need a name.2012-05-15
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    @AndréNicolas: One has to know the codomain in order to determine if a function is surjective, for example. If $f:X\to Y$ with $f(X)=Z\subsetneq Y$, and you want to make a restriction in such a way that you get a surjection, how would you describe that? Or, perhaps more to the point, *what* are you restricting?2012-05-16

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