Question 71850: From the information provided for f(x) and g(x), evaluate (f o g)^-1(2)
x: 1,2,3,4,5
f(x): 3,4,5,1,2
g(x): 5,4,2,3,1
A little help
Found 2 solutions by venugopalramana, ikleyn:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! From the information provided for f(x) and g(x), evaluate (f o g)^-1(2)
x: 1,2,3,4,5
f(x): 3,4,5,1,2
g(x): 5,4,2,3,1
A little help
G^(-1)[2]=...THAT IS WHEN G(X)=2..WHAT IS X?...WE GET X=3...SINCE G(3)=2
NOW FOF[{G INVERSE OF (2)}]=FOF[3]=4
Answer by ikleyn(54034)  (Show Source):
You can put this solution on YOUR website! .
From the information provided for f(x) and g(x), evaluate (f o g)^-1(2)
x: 1,2,3,4,5
f(x): 3,4,5,1,2
g(x): 5,4,2,3,1
A little help
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The solution in the post by @venugopalramana is incorrect.
I came to bring a correct solution.
To evaluate (f o g)^-1(2), we should find a value of 'x' in the given set { 1, 2, 3, 4, 5 }
(first line of the table) such that
f(g(x)) = 2. (1)
Now look at the table: you see that function 'f' has the value of '2' if and only if
the argument of 'f' is 5.
Thus, we conclude that in order to satisfy equation (1), g(x) must have a value of 5.
Again, look at the table: you see that function 'g' has the value of 5 if and only if the argument of 'g' is 1.
Thus, we got the value of x which is the solution to equation (1).
ANSWER. (f o g)^-1(2) = 1.
CHECK. According to the table, g(1) = 5, and then f(5) = 2. Thus, equation (1) is satisfied.
It means that (f o g)(1) = 2, so (f o g)^-1(2) = 1 is proved.
Solved correctly with complete explanation.
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