函数f:{1,2,3} {1,2,3}满足f(f(x))=f(x),则这样的函数个数为( )
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考虑兆扮值族洞灶域有多少个元素得到对应:
若是3个,则得到f(x) = x
若是2个,则 f(1) = 1,f(2) = 3,f(3) = 3; f(1) = 1,f(2) = 1,f(3) =3;
f(1) = 1,f(2) = 2,f(3) = 2; f(1) = 1,f(2) = 2,f(3) = 1
f(1) = 2,f(2) = 2,f(3) = 3;
f(1) = 3,f(2) = 2,f(3) = 3;
若是1个,则f(1) = f(2) = f(3) = 1,这样的函数有颤裤3个.
所以总共10个
若是3个,则得到f(x) = x
若是2个,则 f(1) = 1,f(2) = 3,f(3) = 3; f(1) = 1,f(2) = 1,f(3) =3;
f(1) = 1,f(2) = 2,f(3) = 2; f(1) = 1,f(2) = 2,f(3) = 1
f(1) = 2,f(2) = 2,f(3) = 3;
f(1) = 3,f(2) = 2,f(3) = 3;
若是1个,则f(1) = f(2) = f(3) = 1,这样的函数有颤裤3个.
所以总共10个
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