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1.问题提出的背景很多与《全日制普通高级中学教科书(必修·第一册(上)》配套的资料上,都有这样一类题目:求函数y=1/x2-6x+1的值域. 大多数学生是这样回答的:因为x2-6x+ 1=(x-3)2-8≥-8, 所以1/x2-6x+1 ≤-1/8,即原函数的值域是{y|y≤-1/8}. 类似的错误经过反复讲评、订正,但收效甚微.于是决定以“探讨y=1/f(x)型函数的值域”为课题上一堂专题课.
1. Background of the problem Many of the materials that are included in the “Full-time Ordinary High School Textbook (Compulsory First Book (upper)” have such a problem: Find the value of the function y = 1/x2-6x+1. Domain. Most students answer this question: Since x2-6x+ 1=(x-3)2-8≥-8, 1/x2-6x+1 ≤-1/8, ie the range of the original function is { y|y ≤ -1/8}. Similar errors have been repeatedly reviewed and revised, but with little success. Therefore, it was decided to explore the value domain of y = 1/f(x) type functions with the topic of “”. class.