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Question
Answer the following:
Find composite of f and g:
f = {(1, 3), (2, 4), (3, 5), (4, 6)}
g = {(3, 6), (4, 8), (5, 10), (6, 12)}
Solution
f = {(1, 3), (2, 4), (3, 5), (4, 6)}
g = {(3, 6), (4, 8), (5, 10), (6, 12)}
∴ f(1) = 3, f(2) = 4, f(3) = 5, f(4) = 6
∴ g(3) = 6, g(4) = 8, g(5) = 10, g(6) = 12
(g ° f) (x) = g(f(x))
(g ° f) (1) = g (f(1)) = g (3) = 6
(g ° f) (2) = g (f(2)) = g (4) = 8
(g ° f) (3) = g (f(3)) = g (5) = 10
(g ° f) (4) = g (f(4)) = g (6) = 12
∴ g ° f = {(1, 6), (2, 8), (3, 10), (4, 12)}
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