Let A={1,2,3,4,5} and B={6,7,8,9,10,11,12}.

How many functions f:A->B are such that f -1({6,7,8})={1,2}?

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- Nov 9th 2009, 01:03 PMsbankicafunction composition and inverse function
Let A={1,2,3,4,5} and B={6,7,8,9,10,11,12}.

How many functions f:A->B are such that f -1({6,7,8})={1,2}? - Nov 9th 2009, 01:29 PMPlato
Any function $\displaystyle \phi :\{ 1,2\} \mapsto \{ 6,7,8\}$ is such that $\displaystyle \phi ^{ - 1} \{ 6,7,8\} = \{ 1,2\} $.

There are $\displaystyle 3^2$ such functions. WHY?

How many functions $\displaystyle \{ 3,4,5\} \mapsto \{ 9,10,11,12\}?$

Can you answer the question posted? - Nov 9th 2009, 01:33 PMsbankica
4^3?

- Nov 9th 2009, 01:34 PMsbankica
so answer is: (3^2)(4^3)

- Nov 9th 2009, 01:41 PMPlato
- Nov 9th 2009, 08:13 PMoldguynewstudent
- Nov 10th 2009, 03:07 AMPlato
$\displaystyle \left\{ {\left( {1,6} \right),\left( {2,6} \right)} \right\},\,\left\{ {\left( {1,7} \right),\left( {2,7} \right)} \right\},\,\left\{ {\left( {1,8} \right),\left( {2,8} \right)} \right\}$

$\displaystyle \left\{ {\left( {1,6} \right),\left( {2,7} \right)} \right\},\,\left\{ {\left( {1,6} \right),\left( {2,8} \right)} \right\},\,\left\{ {\left( {1,7} \right),\left( {2,6} \right)} \right\}$

$\displaystyle \left\{ {\left( {1,7} \right),\left( {2,8} \right)} \right\},\,\left\{ {\left( {1,8} \right),\left( {2,6} \right)} \right\}\;\& \,\left\{ {\left( {1,8} \right),\left( {2,7} \right)} \right\}$ - Nov 10th 2009, 12:18 PMoldguynewstudent