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近年来,数学高考试题中开始出现不动点问题.不动点的定义是指:若函数f(x)对其定义域上的某一点x0,有f(x0)=x0,则称x0是f(x)的一个不动点.不动点问题通常以不动点为载体,与函数、数列、不等式、解析几何的知识进行综合,结合数学思想、方法,与时代信息融为一体,考查学生综合解决问题的能力.不动点问题设问情境新颖、独到,而教材上又未过多地涉及.本文试图对不动点问题的解题途径、规律和策略进行探索,权当对教材的补充.
In recent years, the problem of fixed points began to appear in the mathematics examination questions. The definition of fixed point means that if the function f(x) has f(x0)=x0 at a certain point x0 on its domain, then x0 is said to be A fixed point of f(x). The fixed point problem is usually based on the fixed point, and is integrated with the knowledge of functions, series, inequalities, analytical geometry, combined with mathematical thoughts and methods, integrated with the information of the times, and examined. Student’s ability to solve problems comprehensively. The fixed point problem is novel and unique, and the teaching material has not been involved too much. This article attempts to explore the problem-solving approaches, rules, and strategies of the fixed point problem. The supplement.