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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 g ° f
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Solution
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
g ° f : {2, 4, 5} → {2, 4}
(g ° f) (2) = g(f(2)) = g(3) = 4
(g ° f) (4) = g(f(4)) = g(6) = 2
(g ° f) (5) = g(f(5)) = g(2) = 4
∴ g ° f = {(2, 4), (4, 2), (5, 4)}
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