Question

Let f: (2, 4, 5} → {2, 3, 6} and g: {2, 3, 6} → {2, 4} be given by f = {(2, 3), (4, 6), (5, 2)} and g = {(2, 4), (3, 4), (6, 2)}. Write down gof.

Answer 1

f = {(2, 3), (4, 6), (5, 2)}

∴ f(2) = 3, f(4) = 6, f(5) = 2

g ={(2, 4), (3, 4), (6, 2)}

∴ g(2) = 4, g(3) = 4, g(6) = 2

gof: {2, 4, 5} → {2, 4}

(gof) (2) = g(f(2)) = g(3) = 4

(gof) (4) = g(f(4)) = g(6) = 2

(gof) (5) = g(f(5)) = g(2) = 4

∴ gof = {(2, 4), (4, 2), (5, 4)}