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本文对现行六年制高级中学课本代数第一节(下简称课本)“反函数”一节的教学中两个值得注意的问题发表一些肤浅的看法,不妥之处请同志们批评指正。一、反函数的求法课本第73页的小结中指出:“由y=f(x)求y=f~(-1)(x)的步骤是:(1)由y=f(x)中解出x=f~(-1)(y);(2)把x=f~(-1)(y)改写为y=f~(-1) (X)。”与课本配套的教参对此又作了特别的强调:“一.先将y=f(x)看成方程,解出x=f~(-1)(y);二.再互换x、y得到所求的反函数y=f~(-1)(x)。”课本第50页的例题解答全部是按照上述两步进行的,虽然结果正确,但仅限于这
This article presents some superficial views on two issues worthy of attention in the teaching of the “Anti-Functional” section of the first six-year high school textbook algebra section I (hereinafter referred to as “textbooks”), and it is inappropriate for comrades to criticize and correct them. First, the inverse function of the method The textbook summary on page 73 states: “The steps from y=f(x) to y=f~(-1)(x) are: (1) From y=f(x) Solve x=f~(-1)(y); (2) Rewrite x=f~(-1)(y) to y=f~(-1)(X).” A special emphasis was placed on this: “I. First treat y=f(x) as an equation and solve for x=f~(-1)(y); 2. Exchange x and y to get the desired Inverse function y=f~(-1)(x).” The textbook examples on page 50 are all based on the above two steps. Although the result is correct, it is limited to this