solution:

Given capacity, 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)}

Find gof.

At f(1) = 2 and g(2) = 3, gof is

gof(1) = g(f(1)) = g(2) = 3

At f(3) = 5 and g(5) = 1, gof is

gof(3) = g(f(3)) = g(5) = 1

At f(4) = 1 and g(1) = 3, gof is

gof(4) = g(f(4)) = g(1) = 3

In this way, gof = {(1,3), (3,1), (4,3)}