Functional composition

For functions f: A -> B and g: B -> C, the functional composition of function f and function g is the function (g o f): A -> C, defined by (g o f)(x) = g(f(x)). For example, if f : {1,2,3} -> {A,B,C,D} and g : {A,B,C,D} -> {4,5}, the composition of g(y)=y2 and f(x)=x+1 is (g o f)(x)=(x+1)2.

Function composition is applying a function to the results of another function. So, in (g o f)(x) = g(f(x)), first apply f(), and then g(). Some functions can be decomposed into two (or more) simpler functions.