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贵刊1988年第1期《灵活使用奇、偶函数的定义》一文中,张老师提出:“今后在判断或证明函数的奇偶性时,除了按课本定义直接指出的f(-x)=f(x)[应该是f(-x)=±f(x)]的方法处理外,有时根据题目特点还可以按f(-x)±f(x)=0灵活处理,这样可以扩大解题思路。”此见解很有可取之处。但我认为,这样的提法不足以使学生真正灵活使用函数奇偶性定义准确地判断一般初等函数的奇偶性,容易出现形式上的套用现象,因此适当地说明一下奇偶函数定义中的问题是必要的。一、奇偶函数的定义域必须是关于原点的对称区间。如判断函数f(x)=(1+sin2x)∶(cos~2x+sinx·cosx)-1的奇偶性。按张老师所提供的方法处理如下:
In the article “Defining the Use of Odd and Even Functions” in the first issue of 1988, Professor Zhang suggested: “In the future, when judging or proving the parity of a function, f(-x)=f directly pointed out in the textbook definition. (x) [It should be f (-x) = ± f (x)] method of processing, sometimes according to the characteristics of the problem can also be flexibly handled by f (-x) ± f (x) = 0, which can expand the problem Ideas.” This opinion is very good. However, I think that such a formulation is not enough to make students truly flexible to use the function parity definition to accurately determine the parity of general elementary functions, and it is prone to formal application. Therefore, it is necessary to properly explain the problems in the definition of parity functions. of. First, the domain of the parity function must be symmetrical about the origin. For example, determine the parity of the function f(x)=(1+sin2x):(cos~2x+sinx·cosx)-1. According to the method provided by Zhang teacher, it is processed as follows: