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1.反函数的存在基础是对应f为一一对应,那么如何判断所给的对应f是否为一一对应呢? 答方法有: 第一,依据一一对应的定义,逐条加以检验。f为从集合A到集合B的一一对应,须满足下列三个条件:(ⅰ)f是从A到B的单值对应;(ⅱ)对A中不同的元素,在B中有不同的象;(ⅲ)B中每一个元素都有原象。如对应f:x→f(x):x+1,x∈N,f(x)∈N。
1. The existence of inverse function is based on the fact that the corresponding f is a one-to-one correspondence, then how to determine whether the given corresponding f is a one-to-one correspondence? A method is: First, based on the definition of one-to-one correspondence, one by one to test. f is a one-to-one correspondence from set A to set B. The following three conditions must be satisfied: (i) f is a single-valued correspondence from A to B; (ii) different elements in A are different in B. (iii) Each element in B has an original image. For example, f:x→f(x):x+1,x∈N,f(x)∈N.