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Restriction of a function

In mathematics, the restriction of a functionf{\displaystyle f} is a new function, denoted f|A{\displaystyle f\vert _{A}} or f↾A,{\displaystyle f{\upharpoonright _{A}},} obtained by choosing a smaller domainA{\displaystyle A} for the original function f.{\displaystyle f.} The function f{\displaystyle f} is then said to extendf|A.{\displaystyle f\vert _{A}.}Formal definitionLet f:E→F{\displaystyle f:E\to F} be a function from a setE{\displaystyle E} to a set F.{\displaystyle F.} If a set A{\displaystyle A} is a subset of E,{\displaystyle E,} then the restriction of f{\displaystyle f}to A{\displaystyle A} is the function f|A:A→F{\displaystyle {f|}_{A}:A\to F} given by f|A(x)=f(x){\displaystyle {f|}_{A}(x)=f(x)} for x∈A.{\displaystyle x\in A.} Informally, the restriction of f{\displaystyle f} to A{\displaystyle A} is the same function as f,{\displaystyle f,} but is only defined on A{\displaystyle A}.

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