Properties and Applications of Some Algebraic Transformations from the Conditional Function

The intended purpose of this paper is to associate with a given function y = f(x) whose derivative admits one to three turning points an infinite number of other functions, called conditional functions (Cdf ),which are related to f in a way similar to that of a bijective function and its inverse. However, the new application called conditional function is defined for both bijective and non bijective functions. The composite map of f and its conditional function is called a transformation, and some applications of these transformations presented in the paper include amongst others, the determination of analytic solutions for a number of algebraic equations describing the dynamics of natural phenomena.