Restriction of a function

In mathematics, the restriction of a function f is a new function ${\displaystyle f\vert _{A}}$ obtained by choosing a smaller domain A for the original function ${\displaystyle f}$. The notation ${\displaystyle f{\upharpoonright _{A}}}$ is also used.

Let ${\displaystyle f:E\to F}$ be a function from a set E to a set F, so that the domain of f is in E (${\displaystyle \mathrm {dom} \,f\subseteq E}$). If a set A is a subset of E, then the restriction of ${\displaystyle f}$ to ${\displaystyle A}$ is the function

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