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现将反函数教学中学生感到困惑的一些问题,作一些回答。不对之处望指正。一、问:函数x=∫~(-1)(y)和函数y=∫~(-1)(x)是同一个函数,还是两个不同的函数? 答:是同一个函数。因为函数三要素是定义域、值域及定义域对值域上的映射。而对使用什么字母作自变量,什么字母表示函数并没有限制。当没有指明函数的定义域时.一般是指使表达式有意义的自变量构成的集合。在函数x=∫~(-1)(y)和函数y=∫~(-1)(x)中,定义域都是使其有意义的实数的集合,从而相等,且映射相同,值域也就相同了。但是,如果将x=∫~(-1)(y)和y=∫~(-1)(x)作为方程看,这两者就不是同一个方程了,若x=u y=v是x=∫~(-1)(y)的解,则x=v y=u才是y=∫~(-1)(x)的解。
Now I will give some answers to some of the questions that students in the anti-function teaching are puzzled by. Do not correct me. Q. Is the function x=∫(-1)(y) and the function y=∫(-1)(x) the same function, or two different functions? A: It is the same function. Because the three elements of the function are the mapping of the definition domain, the value domain, and the definition domain to the value domain. There is no limit to what letter represents the function of which letter is used as an independent variable. When the domain of the function is not specified, it is generally a set of independent variables that make the expression meaningful. In the function x=∫~(-1)(y) and the function y=∫~(-1)(x), the definition domain is a set of real numbers making it meaningful so that they are equal, and the mapping is the same. It’s the same. However, if we look at x=∫~(-1)(y) and y=∫~(-1)(x) as equations, the two are not the same equation, if x=uy=v is x= If ∫~(-1)(y) is solved, then x=vy=u is the solution to y=∫~(-1)(x).