关于反函数有以下众所周知的性质:函数y=f(x),x∈A(y∈C)的图象与它的反函数y=f-1(x),x∈C(y∈A)的图象关于直线y=x对称.近期发现有多家杂志提及到了它的逆命题:如果两个函数的图象关于直线y=x对称,那么这两个函数是互为反函数.这几家杂志的作者的观点均以为这是一个假命题,但都没有反例显示.笔者考虑到这是一个有意思的问题,很 The inverse function has the well-known property that the image of the function y = f (x), x∈A (y∈C) and its inverse function y = f-1 (x), x∈C (y∈A) Image Symmetry on Line y = x Recently several magazines have reported its inverse conjecture: If the images of two functions are symmetric with respect to the line y = x, then these two functions are mutually inverse functions. The view of the authors of several magazines that this is a fake proposition, but none of the examples show that I consider this is an interesting question, it is