Question

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（ ）

Answer 1

考虑值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3个.
所以总共10个