역함수의 존재성에 관한 예비수학교사들의 이해

Abstract

Objectives In this study, this study examined how preservice mathematics teachers express the domains, codomains and ranges of linear functions, quadratic functions, rational functions, irrational functions, exponential functions and logarithmic functions, and how they determined the existence of inverse functions of linear functions, quadratic functions, rational functions, irrational functions, exponential functions and logarithmic functions.
 Methods We investigated 56 preservice mathematics teachers. The responses of preservice mathematics teachers were inductively analyzed, and the meaning was interpreted through in-depth descriptions according to the type of response.
 Results First, most of the preservice mathematics teachers showed the aspect of describing the codomain of a function which codomain was not presented was a set or range of all real numbers. But some preservice mathematics teachers described the codomain as a range though the quadratic function was not a one-to-one function. Second, preservice mathematics teachers described the quadratic function had an inverse functinon and the rational function and irrational function had no inverse function. Third, most preservice mathematics teachers expressed the inverse functions of exponential and logarithmic functions were accurately.
 Conclusions Most of the preservice mathematics teachers showed the aspect of describing the codomain of a function which codomain was not presented was a set or range of all real numbers, and preservice mathematics teachers had a misconception about the existence of an inverse function.