5.
给定集合\(A_{n}=\{1,2,3,...n\}\),映射\(f:A_{n}→A_{n}\)满足:
\(①\)当\(i\),\(j∈A_{n}\),\(i\neq j\)时,\(f(i)\neq f(j)\); \(②\)任取\(m∈An\),若\(m\geqslant 2\),则有\(m∈\{f(1),f(2),...f(m)\}\).
则称映射\(f:A\)\(n\)\(→A\)\(n\)是一个“优映射”\(.\)例如:用表\(1\)表示的映射\(f:A\)\(3\)\(→A\)\(3\)是一个“优映射”.
表\(1\)
\(i\) | \(1\) | \(2\) | \(3\) |
\(f(1)\) | \(2\) | \(3\) | \(1\) |
表\(2\)
\(i\) | \(1\) | \(2\) | \(3\) | \(4\) |
\(f(i)\) | | \(3\) | | |
\((1)\)已知表\(2\)表示的映射\(f:A\)\(4\)\(→A\)\(4\)是一个优映射,请把表\(2\)补充完整\((\)只需填出一个满足条件 的映射\()\);
\((2)\)若映射\(f:A\)\(10\)\(→A\)\(10\)是“优映射”,且方程\(f(i)=i\)的解恰有\(6\)个,则这样的“优映射”的个数是____.