Question 95686: From the information in the table providing values of f(x) and g(x), evaluate (f *g) ^1 (3) the table of
.. x = 1, 2, 3, 4, 5 the table of
f(x) = 5, 3, 5, 1, 2 and the table
g(x) = 4, 5, 1, 3, 2.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! .. x = 1, 2, 3, 4, 5 the table of
f(x) = 5, 3, 5, 1, 2 and the table
g(x) = 4, 5, 1, 3, 2.
Find (f *g) ^1 (3)
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Comment: I'm going to assume you do not mean *, you mean o
which is the composite of the functions.
[(fog)^-1(3)] = [g^-1of^-1](3))
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2nd Comment: What does f^-1 mean?
1st: the function "f" relates values on the "x" line above to values
on the "f" line which is below it. Example: f(3)=5.
2nd: f^-1 reverses the process. Example: f^-1(5)=3
3rd: Similarly g(3)=1, so g^-1(1)=3
Ingeneral, f and g are read from the x-level down to the f or g level
So f^-1 and g^-1 are read from the f or g level UP to the x-level.
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3rd Comment: What is [(f)o(g)]^-1 ?
To activate fog(x) you first find g(x) then apply f to the result
To activeate [fog]^-1 you fist must get rid of the effect of f then the effect
of g so [fog]^-1 = [g^-1 o f^-1](x)
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[g^-1 o f^-1](3) = [g^-1[f^-1(3)]]
Now, note that f^-1(3) = 2 because you go from the
f level UP to the x level.
= [g^-1[2]]
Then, note that g^-1(2) = 5 because you go from the
g level UP to the x level
= 5
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Hope this helps.
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Cheers,
Stan H.
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