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所谓抽象函数问题,就是不给出函数的解析式,而是给出该函数的一些性质,让人们根据这些性质去证明该函数还有哪些性质,或求由该函数所构成的不等式的解集等问题.在这些抽象函数问题中,有一类问题是给出的条件中,有一个该函数满足的函数方程.这就给我们提供了信息,说明该函数实际上是以某个基本初等函数为背景而抽象出来的函数.这个函数不妨称之为背景函数.对这类抽象函数问题如果能找出它的背景函数,仿照背景函数解题方法,这类题就容易解决了,下面通过两例来说明这类问题的解题思路.
The so-called abstract function problem is not to give the analytical formula of the function, but to give some properties of the function, let people prove the properties of the function according to these properties, or find the solution set of inequalities formed by the function. Problems such as these. Among these abstract function problems, there is a class of problems that is given in the conditions, there is a functional equation that the function satisfies. This gives us information that the function is actually a basic elementary function The function abstracted out from the background. This function may be called a background function. If such an abstract function problem can find out its background function and follow the background function problem solving method, such questions can be easily solved. The following two examples are adopted. To illustrate the problem-solving ideas for this type of problem.