Domain

Definition

The domain of a function is the set into which all of the input of the function is constrained to fall. It is the set $X$ in the notation $f:X \rightarrow Y$, and is alternatively denoted as $\text{dom }\left. (f) \right.$.

The above graphic shows a function $f$ from $X$ to $Y$. The blue oval $Y$ is the codomain of $f$. The red oval $X$ is the domain of $f$. The blue oval $Y$ is the codomain of $f$. The yellow oval inside $Y$ is the image of $f$.