\begin{definition}[Definition:Real Function/Domain]
Let $S \subseteq \R$.
Let $f: S \to \R$ be a real function.
The domain of $f$ is the set $S$.
It is frequently the case that $S$ is not explicitly specified. If this is so, then it is understood that the domain is to consist of ''all'' the values in $\R$ for which the function is defined.
This often needs to be determined as a separate exercise in itself, by investigating the nature of the function in question.
\end{definition}