SOLUTION: Let f= 1 2 3 4 5 2 3 1 5 4 and g= 1 2 3 4 5 3 4 2 5 1. What is f inverse -1? Write fog as a product of disjoint cycles.Is fog even?why?

Algebra ->  Functions -> SOLUTION: Let f= 1 2 3 4 5 2 3 1 5 4 and g= 1 2 3 4 5 3 4 2 5 1. What is f inverse -1? Write fog as a product of disjoint cycles.Is fog even?why?       Log On


   

Question 38520: Let f= 1 2 3 4 5
2 3 1 5 4
and

g= 1 2 3 4 5
3 4 2 5 1.
What is f inverse -1?
Write fog as a product of disjoint cycles.Is fog even?why?
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let f= 1 2 3 4 5
2 3 1 5 4
and

g= 1 2 3 4 5
3 4 2 5 1.
What is f inverse -1?

f%5E-1+
= (1 2 3 4 5)
(3 1 2 5 4)

Write fog as a product of disjoint cycles.Is fog even?why?
if you define fog (x) = f(g(x)) then
fog =
(1 2 3 4 5)
(1 5 3 4 2)
as disjoint cycles, it is
(2 ,5)
one transpoition, hence it is odd.
You have to work hard.

Kenny