Let f = {(1,2), (2,3), (3,5), (4,7)} and g = {(1,4), (2,3), (3,1)}
Express each composite as a set of ordered pairs.
a) f of g
To determine the composite function f of g, we need to substitute the outputs of the function g into the function f.
According to the given information, the function g has the following mappings:
g = {(1,4), (2,3), (3,1)}.
We need to substitute these values into the function f = {(1,2), (2,3), (3,5), (4,7)}.
Starting with the first mapping in g, (1,4):
We find the corresponding mapping in f for the output value of 4 in g, which is (4,7).
So, the first mapping in the composite function f of g is (1,7), obtained by replacing the input value 1 from g with the corresponding output value 7 from f.
Similarly, we repeat this process for the other mappings in g:
For (2,3) in g, we find the corresponding mapping in f for the output value of 3 in g, which is (3,5).
So, the second mapping in the composite function f of g is (2,5).
For (3,1) in g, we find the corresponding mapping in f for the output value of 1 in g, which is (1,2).
So, the third mapping in the composite function f of g is (3,2).
Hence, the composite function f of g can be expressed as the set of ordered pairs:
f(g) = {(1,7), (2,5), (3,2)}.