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我们已经熟知“函数y=f(x)的图像和它的反函数y=f~(-1)(x)的图像关于直线y=x对称”这个重要结论,但是关于函数y=f(x)与y=f~(-1)(x)的交点问题,不少同学在认识上存在一定的误区.误区1函数y=f(x)及其反函数y=f~(-1)(x)图像的交点,一定在直线y=x上.我们举两个反例加以阐释.
We are already familiar with the important conclusion that the image of the function y = f (x) and the image of its inverse function y = f ~ (-1) (x) are symmetric about the line y = x, "but for the function y = f (x) and y = f ~ (-1) (x), many students have certain misunderstandings in their cognition. The error function y = f (x) and its inverse function y = f ~ ) (x) The point of intersection of the image must be on the line y = x. Let us take two counterexamples to explain.