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Let f: {3, 9, 12} → {1, 3, 4} and g: {1, 3, 4, 5} → {3, 9} be defined as f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3), (4, 9), (5, 9)}.

Find (i) (g o f) (ii) (f o g)

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(i) We know that domain (g o f) = domain (f) = {3, 9, 12}

By substituting the values

(g o f) (3) = g{f(3)} = g{1} = 3

(g o f) (9) = g{f(9)} = g{3} = 3

(g o f) (12) = g{f(12)} = g{4} = 9

Hence, g o f = {(3, 3), (9, 3), (12, 9)}

(ii) We know that domain (f o g) = domain (g) = {1, 3, 4, 5}

By substituting the values

(f o g) (1) = f{g(1)} = f{3} = 1

(f o g) (3) = f{g(3)} = f{3} = 1

(f o g) (4) = f{g(4)} = f{9} = 3

(f o g) (5) = f{g(5)} = f{9} = 3

Hence, f o g = {(1, 1), (3, 1), (4, 3), (5, 3)}

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