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含特称量词的“存在性”函数综合题是高考和各类考试的常见题型,此类题一般考查学生的逻辑思维的灵活性,通常用集合的思想解这类题,即将问题中两个函数的值域用集合表示,再研究这两个集合之间的关系.下面以高考题为例说明如何用“集合”的观点研究“存在性”问题.
The “Existential” function comprehensive test with special weighing words is a common type of exams in college entrance examination and various examinations. Such examinations usually examine the students’ flexibility in logical thinking. In the question, the range of the two functions is represented by a set, and then the relationship between the two sets is studied. The following example shows how to study the problem of “existence” with the view of “set”.