Definition:Real Function/Domain

Definition
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.