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成题,不是陈题,而是久经考验的、具有典型性、代表性和创造力的好题.成题包括选择题、填空题和解答题(综合题).许多解答题因为内涵深刻,外延广阔,因此格外具有独特的魅力.我们先来欣赏以下几例成题的魅力.[例1]设f(x)是定义在[-1,1]上的奇函数,g(x)的图象与f(x)的图象关于直线x=1对称,当x∈[2,3]时,g(x)=-x~2+4x+c(c为常数),(1)求f(x)的表达式;(2)对于任意的x_1、x_2∈[0,1],且x_1≠x_2,求证:|f(x_2)-(x_1)|<2|x_2-x_1|;(3)对于任意的x_1、x_2∈[0,1],且x_1≠x_2,求证:|f(x_2)-f(x_1)|≤1.[解析]题型有点儿熟,但细细读来,又有了变化.不要去硬背做过的考题,我们来慢慢思考.
Cheng Cheng, not the Chen title, but the proven, typical, representative and creative good topics into multiple choice questions, fill in the blank questions and answer questions (comprehensive questions). Many answer questions because of profound meaning, extension Therefore, let us first appreciate the charm of the following examples: [Example 1] Let f (x) be the odd function defined on [-1,1] and the graph of g (x) (X) = - x ~ 2 + 4x + c (c is a constant) when x∈ [2,3], (1) Find f (x); (2) For any x_1, x_2∈ [0,1] and x_1 ≠ x_2, prove that | f (x_2) - (x_1) | <2 | x_2-x_1 | ) For any x_1, x_2∈ [0,1], and x_1 ≠ x_2, prove: | f (x_2) -f (x_1) | ≤ 1. [Resolved] The questions are a bit familiar, There have been changes. Do not go hard to do the exam, let’s think slowly.