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反函数是中学数学的重要概念,是高考中常考的知识点之一.有关反函数问题大都是以选择题及填空题的形式出现,相对来说,比较容易.本文对反函数的性质进行概括并结合具体例子对利用反函数的性质解决函数问题进行探讨,以求揭示巧用反函数对函数问题求解的一般规律.一、基本性质1.存在性:只有定义域和值域一一映射的函数才有反函数.2.互逆性:原函数的定义域、值域分别是它的反函数的值域、定义域.3.对称性:函数y=f(x)与其反函数y=f-1(x)的图象关于y=x
The inverse function is one of the important concepts in high school mathematics and one of the most commonly used knowledge in college entrance examination.About the inverse function problems are mostly in the form of multiple choice questions and blank fill questions, relatively speaking, it is relatively easy.This paper summarizes the properties of inverse functions In order to reveal the general law of using the inverse function to solve the function problem, this paper discusses the problem of using the function of the inverse function in combination with concrete examples.One, the basic property 1. Existence: Only one domain of the domain of definition and the range of one The function has an inverse function .2 reciprocity: the original function of the domain, the value range is its inverse function of the value domain, the domain.3 Symmetry: function y = f (x) and its inverse function y = The image of f-1 (x) is about y = x