question_answer 30)

Let f : {1, 3, 4}  {1, 2, 5} and g : {1, 2, 5}  {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.  

Answer:

Given f = {(1, 2), (3, 5), (4, 1)}             Here Rf = {1, 2, 5} = Dg and Df = {1, 3, 4}             Now, (gof) (1) = g(f(1)) = g(2) = 3       (gof)(3) = g(f(3)) = g(5) = 1       (fog) (4) = g(f(4)) = g(1) = 3       So, gof = {(1, 3), (3,1), (4,3)}