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Question
Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = ______ and f o g = ______.
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Solution
Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = {(1, 3), (3, 1), (4, 3)} and f o g = {(2, 4), (5, 2), (1, 5)}.
Explanation:
Given that, f = {(1, 2), (3, 5), (4, 1)} and g = ((2, 3), (5, 1), (1, 3)}
∴ gof(1) = g{f(1)} = g(2) = 3
gof(3) = g{f(3)} = g(5) = 1
gof(4) = g{f(4)} = g(1) = 3
∴ gof(x) = {(1, 3), (3, 1), (4, 3)}
Now, fog(2) = f{g(2)} = f(3) = 5
fog(5) = f{g(5)} = f(1) = 2
fog(4) = f{g(1)} = f(3) = 5
fog = {(2, 4), (5, 2), (1, 5)}
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