Problem:
Let f= {(1,2), (2,3), (3,4), (4,1)} and g= {(1,3), (2,1), (3,4), (4,2),(5,1).
Find f-1 and g o f.
Is g one-to-one?
Explain
You just have to look into what your numbers are transformed by the functions.
is permutation ( ), and it is a cycle.
, so , that is to say .
is a function from to .
. So , with the set notation. Just find the others elements of .
What can you say about and ? Then conclude.