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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.
Solution
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)}`
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