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思维的严密性贯穿于高中数学学习的始终。函数的定义域是构成函数的两大要素之一,函数的定义域(或变量的允许值范围)似乎是非常简单的,然而在解决问题中不加以注意,常常会使人误入歧途。在解函数题中强调定义域对解题结论的作用与影响,对提高学生的数学思维严密性是十分有益的。
The rigor of thinking runs through high school mathematics learning. The domain of a function is one of the two major elements that make up a function. The scope of a function (or range of allowed values for a variable) seems to be very simple. However, paying no attention to solving a problem often leads astray. It is helpful to improve students' mathematic thinking rigor by emphasizing the role and influence of domain definition in the solution function.