Domain

A domain is the set of inputs of a function: if $f:A\to B$ is a function , then its domain is the set $A$.

Changing the domain (for example by taking a restriction ) produces a new function, even if the output rule looks the same. The elements of the domain appear as the first components of ordered pairs in the graph of $f$.

Examples:

• For $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=x^2$, the domain is $\mathbb{R}$ (the real numbers ).
• For the inclusion map $i:S\to A$ with $S\subseteq A$, the domain is $S$.