Question 1200475: If f(x) = {(2, 3), (4, 8), (7, - 1)} and g(x) = {(8, 2), ( - 1, 4), (2, 7)},
find (f o g)(x), if it exists.
Answer by math_tutor2020(3817)   (Show Source):
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Answer: (f o g)(x) = {(8,3), (-1,8), (2,-1)}
Explanation:
(f o g)(x) is the same as f( g(x) )
The g(x) function is
g(x) = {(8,2), (-1,4), (2,7)}
which means
g(8) = 2
g(-1) = 4
g(2) = 7
Each of those outputs (2,4 and 7) must be an input for the f(x) function to have f(g(x)) be possible.
Luckily that is indeed the case.
f(x) = {(2,3), (4,8), (7,-1)}
breaks down to
f(2) = 3
f(4) = 8
f(7) = -1
Let's rewrite those three items above to involve g(x)
f(2) = 3 ---> f(g(8)) = 3
f(4) = 8 ---> f(g(-1)) = 8
f(7) = -1 ---> f(g(2)) = -1
In short,
f(g(8)) = 3
f(g(-1)) = 8
f(g(2)) = -1
or
(f o g)(8) = 3
(f o g)(-1) = 8
(f o g)(2) = -1
Therefore,
(f o g)(x) = {(8,3), (-1,8), (2,-1)}
Here's the input/output mapping diagram for each function piece.
Start at the left side and move toward the right along the pathway of arrows shown.
For instance, if the input is x = 8, then
g(8) = 2
f(2) = 3 aka f(g(8)) = 3
Therefore, f(g(x)) = 3 when the input is x = 8.
The g(x) function acts as the input to the f(x) function.
Effectively g(x) takes on the role of x so to speak.
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