作业帮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} an
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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} an
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|?
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} an
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|次方=2187,所以|A|=7
3.
f(1)=f(2)=1,f(3)=3
A1={1,3},A2={2,3},则：{3} = f(A1∩A2) ≠ f(A1)∩f(A2) = {1,3}
4.
单射函数,所以根据排列组合中的原理,应该有：P(|B|,|A|)个.
其中P(|B|,|A|)表示|B|个中取|A|个的排列数.
放到这题里,|A|=5,所以|B|=8
我不会