论文部分内容阅读
本文对抽象函数的反函数的求法给出通用方法.一、问题的提出问题Ⅰ:设函数f(x)的反函数是f~(-1)(x),且函数f(2x+3)的反函数存在,求f(2x+3)的反函数.问题Ⅱ:设函数f(x)的反函数是f~(-1)(x),且函数f~(-1)(2x+3)的反函数存在,求f~(-1)(2x+3)的反函数.问题Ⅲ:设函数f(x)的反函数是f~(-1)(x),问:1.哪个函数的反函数是f~(-1)(x-3)/22.哪个函数的反函数是2·f~(-1)(x)+3二:问题的通用解法三个问题实质都是求抽象函数的反函数,可设所求函数为y=g(x),只须求出g(x)即可.而求函数g(x)用到如下结论:
This paper gives a general method to find the inverse function of an abstract function. First, the problem is raised. Question I: Let the inverse function of function f(x) be f~(-1)(x), and the function f(2x+3) The inverse function exists, find the inverse function of f(2x+3). Problem II: Let the inverse function of function f(x) be f~(-1)(x), and the function f~(-1)(2x+ Inverse function of 3) exists, find the inverse function of f~(-1)(2x+3). Question III: Let the inverse function of function f(x) be f~(-1)(x). Q: 1. Which function’s inverse function is f~(-1)(x-3)/22. Which function’s inverse function is 2?f~(-1)(x)+3?: The general solution of the problem Is to find the inverse function of the abstract function, can be set to find the function y = g (x), only to find g (x) can be. Find the function g (x) use the following conclusions: