Question

if f:A-B,g:B-A and f={(1,a),(2,c),(4,d),(3,b)} g'={(2,a),(4,b),(1,c),(3,d)} verify (gof)'=f'og'​

Answer 1

Step-by-step explanation:

Given f={(1,a),(2,c),(4,d),(3,b)} and g−1={(2,a),(4,b),(1,c),(3,d)}.

Then we have f−¹={(a,1),(c,2),(d,4),(b,3)} and g={(a,2),(b,4),(c,1),(d,3)}.

Now gof={(1,2),(2,1),(4,3),(3,4)}

⇒(gof)−1={(2,1),(1,2),(3,4),(4,3)}......(1).

Again f−¹og−¹={(2,1),(4,3),(1,2),(3,4)}={(2,1),(1,2),(3,4),(4,3)}....(2).

From (1) and (2) we have (gof)−¹=f−¹og−¹,