The composition gof, given f=(1,2)(3,4),(5,4) and g=(2,3)(4,3),(6,1), is gof = (1,3)(3,3)(5,1). The elements in f are mapped through g, resulting in the composed permutation.
To find the composition of two functions gof, we apply the function g to the result of applying function f.
In this case, f is the permutation (1,2)(3,4),(5,4) and g is the permutation (2,3)(4,3),(6,1).
To apply g to f, we consider each element in f and apply g to it.
For example, in f, (1,2) maps 1 to 2.
We then apply g to 2, which maps 2 to 3. So, (1,2) in f becomes (1,3) in the composition gof.
Similarly, for the other elements in f, we apply g and obtain the resulting composition:
gof = (1,3)(3,3)(5,1).
Question:
given f=(1,2)(3,4),(5,4) g=(2,3)(4,3),(6,1). Write gof.