22 - Functional Programming GapFill

A function is such that f: A → B, where A is the   parameterinputargumentresult type, and B is the   resultargumentoutputinput type.  A, in this instance, is called the   top-domainsub-domainco-domaindomain, and B is called the   co-domaindomainsub-domaintop-domain, and both are   subsetsparametersbasescoefficients of objects in some data type - real numbers, for example.

Suppose we take the function f(x) = x² + 2x + 3.  For this function, as with any, each value of x can generate   twonooneany number of result(s).

Two functions can be combined in order to create a new function, and this operation is called functional   conjoinmentconcatenationcompositionco-creation.  With two functions f: P → Q and g: Q → R, performing this operation results in a function whose   co-domain is Pdomain is Psub-domain is Qdomain is Q and   domain is Rsub-domain is Rco-domain is Rdomain is Q.