For instance , the functions f : X → Y and g : Y → Z can be composed to yield a function which maps x in X to g ( f ( x ) ) in Z. Intuitively , if z is a function g of y and y is a function f of x , then z is a function of x . The resulting composite function , notated g ∘ f : X → Z -- interchangeably written , in many sources and within this article , as g ∘ f : X → Y -- is defined by ( g ∘ f ) ( x ) = g ( f ( x ) ) for all x in X . The notation g ∘ f is read as `` g circle f '' , or `` g round f '' , or `` g composed with f '' , `` g after f '' , `` g following f '' , or `` g of f '' .
The value of g ∘ f given the input x is written ( g ∘ f ) ( x ) and is defined as g ( f ( x ) ) ( which means our way of writing g composed with f makes sense ) .