Composite Functions

Composite Functions Definition Let f : A → B and g : B → C be two functions. Then the composition of f and g, denoted by g ∘ f, is defined as the function g ∘ f : A → C given by g ∘ f (x) = g(f (x)), ∀ x ∈ A.

The below figure shows the representation of composite functions. The order of function is an important thing while dealing with the composition of functions since (f ∘ g) (x) is not equal to (g ∘ f) (x).

Symbol: It is also denoted as (g∘f)(x), where ∘ is a small circle symbol. We cannot replace ∘ with a dot (.), because it will show as the product of two functions, such as (g.f)(x).