METHODOLOGICAL PRINCIPLES FOR THE DETERMINATION OF INVERSE FUNCTIONS: A REALITY IN SECONDARY

Abstract

The research intention arises from the need to address a problem in the management of the teaching and learning process. The study was developed under the title: Methodological Principles for the Determination of Inverse Functions: A Reality in Secondary Education. The motivation stemmed from the concern that there were uncertain situations regarding whether the inverse function of , defined from onto , should be expressed as  or , or even , as found in various textbooks. This situation defines the research problem, namely: the existence of different notations for the inverse functions of . The objective is to clarify the misconceptions in determining inverse functions, showing that, given a function dependent on , its inverse also depends on . That is, if , its inverse is . Since  is not the correct notation for the inverse of , another procedure is required. Starting from the general notation of a function , one substitutes  with  and  with , obtaining , and then isolates  in terms of , resulting in . Considering  as the inverse of leads to errors in the process of obtaining the inverse function from . Thus, if  is bijective, defined from  onto , then  is also bijective, defined from  onto . Some authors also consider the inverse of  to be , which generates a series of doubts and misconceptions among students, hindering their proper understanding of inverse functions. Therefore, a practical approach is required to resolve this problem.