1.Does formula f(x)=1/(x²-2) define a function f:R->R?A function Z->R?2.If there are 2187 function f:A->B and |B|=3.What is |A|?3.Give an example of a function f:A->B and A1,A2 in the A for which f(A1∩A2) ≠ f(A1)∩f(A2)4.If A={1,2,3,4,5} and there are 6720 injective functions f:A->B,what is |B|?
问题描述：
1.Does formula f(x)=1/(x²-2) define a function f:R->R?A function Z->R?
2.If there are 2187 function f:A->B and |B|=3.What is |A|?
3.Give an example of a function f:A->B and A1,A2 in the A for which f(A1∩A2) ≠ f(A1)∩f(A2)
4.If A={1,2,3,4,5} and there are 6720 injective functions f:A->B,what is |B|?
答
都很简单呀.1.f不是R->R上的函数,因为x=sqrt(2)时,分母等于0.（sqrt代表开根号）但f是Z->R上的函数,因为x取任意整数都不会导致分母为0.2.根据排列组合中的乘法原理,A->B的函数,共有|B|的|A|次方个.也就是说3的|A|次...