Let $f$ and $g$ be permutations on the set $\lbrace 1, 2, 3, 4, 5, 6, 7 \rbrace$, defined as follows

$$f = ( 3\,1\,6\,7 ) ( 1\,4\,5 )$$
$$g = ( 4\,7\,6\,1\,3 )$$
Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. $( 1, 2 ), ( 3, 4, 5 ), \ldots$ ).
Do not include 1-cycles (e.g. $(2)$ ) in your answer.

(a) $fg =$

(b) $f^{-1} =$

(c) $fgf^{-1} =$

Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so $(1,3)(1,2)=(1,2,3)$ not $(1,3,2)$.