Question

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 1

The functions f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} are defined as

f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}.

gof(1) = g(f(1)) = g(2) = 3       [f(1) = 2 and  g(2) = 3]

gof(3) = g(f(3)) = g(5) = 1       [f(3) = 5 and  g(5) = 1]

gof(4) = g(f(4)) = g(1) = 3       [f(4) = 1 and g(1) = 3]

`:. gof = {(1,3),(3,1),(4,3)}`