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本文拟列出几条常见的解数学题的思维模式。一、弄清题意这属于非智力因素的范畴,对大多数学生(甚至是成绩较好的学生)来说,都不是多余的忠告。教学中,我们经常发现学生不明题意就茫然解之,结果或是目的性不明而碰壁或是变换(增加、去掉、更解)条件而导致错误。例1 设函数y=f(x)(x∈R且x≠0),对任意非零的实数x_1、x_2满足f(x_1x_2)=f(x_1)+f(x_2),f(x)在(0,+∞)上为增函数,(1)求证f(1)=f(-1)=0;(2)解不等式f(x)+f(x-1/2)≤0。
This article proposes several common modes of thinking for solving mathematical problems. First, to clarify the meaning of this category is a non-intelligence factor category, for most students (even better students), are not redundant advice. In teaching, we often find that students are confused about their unclear questions. The result is unclear, and the result is unclear, and hitting a wall or changing (adding, removing, and resolving) conditions leads to mistakes. Example 1 Let function y=f(x) (x∈R and x≠0) satisfy f(x_1x_2)=f(x_1)+f(x_2) for any non-zero real number x_1, x_2, f(x) (0, +∞) is an increasing function, (1) verification f(1) = f(-1) = 0; (2) solution inequality f(x) + f(x-1/2) ≤ 0.