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} .