Definition 3.5: Let f be one-to-one correspondence between A and B We say that inverse relation f-l is the everywhere inverse function of f. We denoted f B-A And iff(a)=b then f-(b)=a &o Theorem 3.8: Letf be one-to-one correspondence between A and B. Then the inverse function f-lis also one-to-one correspondence. 8 Proof: (1)f-is onto(f- is a function from B to A For any a∈A, there exists b∈ B such that f(b=a) 冷(2f- is one to one For any b1,b2∈B,ifb1≠b2 then f1(b1)≠f1(b2) 冷IffA→ B is one-to-0 ne correspondence, then f1 B-A is also one-to-one correspondence. The function f is called invertible.❖ Definition 3.5: Let f be one-to-one correspondence between A and B. We say that inverse relation f -1 is the everywhere inverse function of f. We denoted f -1：B→A. And if f (a)=b then f -1 (b)=a. ❖ Theorem 3.8: Let f be one-to-one correspondence between A and B. Then the inverse function f -1 is also one-to-one correspondence. ❖ Proof: (1) f –1 is onto (f –1 is a function from B to A ❖ For any aA,there exists bB such that f -1 (b)=a) ❖ (2)f –1 is one to one ❖ For any b1 ,b2B, if b1b2 then f -1 (b1 ) f -1 (b2 ). ❖ If f:A→B is one-to-one correspondence, then f -1： B→A is also one-to-one correspondence. The function f is called invertible