Restriction of a function

In mathematics, the restriction of a function${\displaystyle f}$ is a new function, denoted ${\displaystyle f\vert _{A}}$ or ${\displaystyle f{\upharpoonright _{A}},}$ obtained by choosing a smaller domain${\displaystyle A}$ for the original function ${\displaystyle f.}$ The function ${\displaystyle f}$ is then said to extend${\displaystyle f\vert _{A}.}$