A function F {\displaystyle F} is said to be an extension of another function f {\displaystyle f} if whenever x {\displaystyle x} is in the domain of f {\displaystyle f} then x {\displaystyle x} is also in the domain of F {\displaystyle F} and f ( x ) = F ( x ) . {\displaystyle f(x)=F(x).} That is, if domain ⁡ f ⊆ domain ⁡ F {\displaystyle \operatorname {domain} f\subseteq \operatorname {domain} F} and F | domain ⁡ f = f . {\displaystyle F{\big \vert }_{\operatorname {domain} f}=f.}