SOLUTION: For the functions f and g, given that f∘g = {(4,3), (­-1,9), (­-2,7)} What is an example of sets of ordered pairs for f and g that fits this information?

If    (a,b) is a member of g 
and   (b,c) is a member of f
then  (a,c) is a member of f∘g

(4,3) is a member of f∘g, so let a=4 and c=3

Since (4,b) is a member of g 
and   (b,3) is a member of f
then  (4,3) is a member of f∘g

We just need to make up a value for b, say 6, then

Since (4,6) is a member of g 
and   (6,3) is a member of f
then  (4,3) is a member of f∘g

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(-1,9) is a member of f∘g, so let a=-1 and c=9

Since (-1,b) is a member of g 
and   (b,9) is a member of f
then  (-1,9) is a member of f∘g

We just need to make up a value for b, say 5, then

Since (-1,5) is a member of g 
and   (5,9) is a member of f
then  (-1,9) is a member of f∘g

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(-2,7) is a member of f∘g, so let a=-2 and c=7

Since (-2,b) is a member of g 
and   (b,7) is a member of f
then  (-2,7) is a member of f∘g

We just need to make up a value for b, say -8, then

Since (-2,8) is a member of g 
and   (8,7) is a member of f
then  (-2,7) is a member of f∘g

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Therefore g = {(4,6), (-1,5), (-2,8)} and
          f = {(6,3),  (5,9),  (8,7)}

is an example of what g and f could be.

Edwin