It is trivial. Say f=(a1,a2,a3) and g=(b1,b2) for simplicity sake. For fg = gf we require that they are the same function. We want to show fg (x) = gf (x). Now if x ! = a_1,a_2,a_3,b_1,b_3 then it says fixed. If x=a1 then fg(a1)=a_2 and gf(a_1)=a_2 because they are disjoint. And the same idea in general.