Composite function or composition of function involves the creation of one function from another function. For instance, if function 'f' relates the variables A and B and function 'g' is relating the variables B and C then it can be said that output of first function is used as input of another function. In other words, functions f: A → B and g: B → C can be created by computing the output of 'g' when it has an argument of f (A) instead of A and if C is a function g (g (C)) of B and B is a function f of A, then C is a function of A. Let’s see figure which shows the composition of f and g.
Thus composite function can be obtained as g∘f: A → C defined by (g ∘ f)(a) = g(f(a)) for all a in A.
Composite function can be noted as "g Circle f" or "g composed with f" or "g after f" or" just "g of f".
Functions composition is always associative. Associative property states that first parenthesis in the function must be solved. That is, if p, q, and r are three functions and they are served with parentheses, then parenthesized functions are solved. Composite functions g and f are said to follow the Commutative Property. Let’s see The Range of Composite Functions. The range of function g is (1, ∞) and Domain of f is (0, ∞) then range of g which intersects the domain of f is (1, ∞). This interval [1,∞ ) is the new domain for f, in other words, we can say that range belonging to the domain of [1,∞) for the function f is [2, ∞). Thus range of composite function (g o f) is (2, ∞).