SOLUTION: I really need some help on this question. from the information in the table providing values of f(x) and g(x), evaluate (f o g)^-1(3) x 1 2 3 4 5 __

: I really need some help on this question.
from the information in the table providing 
values of f(x) and g(x), evaluate (f o g)^-1(3)

  x  1 2 3 4 5
___________________________________________
f(x) 5 3 5 1 2
____________________________________________
g(x) 4 5 1 3 2 

You must have made a mistake because f(x) is
not a one-to-one function since f(1) = 5 and
also f(4) = 5.

I will assume the first 5 on f(x) above should
have been a 4; otherwise inverses involving f
does not exist. Making that change:

x    1 2 3 4 5
___________________________________________
f(x) 4 3 5 1 2
____________________________________________
g(x) 4 5 1 3 2 

From the above we get this

f(1) = 4     g(1) = 4
f(2) = 3     g(2) = 5
f(3) = 5     g(3) = 1
f(4) = 1     g(4) = 3
f(5) = 2     g(5) = 2

(fog)(1) = f( g(1) ) = f(4) = 1
(fog)(2) = f( g(2) ) = f(5) = 2
(fog)(3) = f( g(3) ) = f(1) = 4
(fog)(4) = f( g(4) ) = f(3) = 5
(fog)(5) = f( g(5) ) = f(2) = 3

(fog)(1) = 1 so (fog)-1(1) = 1
(fog)(2) = 2 so (fog)-1(2) = 2
(fog)(3) = 4 so (fog)-1(4) = 3
(fog)(4) = 5 so (fog)-1(5) = 4
(fog)(5) = 3 so (fog)-1(3) = 5

Therefore (fog)-1(3) = 5, choice d.
That is, of course, based on your having made
an error in your copying.  I may have guessed
what it should have been incorrectly.  Also
it is not necessary to find ALL the values of
(fog)-1, but since you are
learning, I thought it better to find 
everything you could have been asked.

Perhaps you were supposed to use the formula:

(fog)-1(x) = (g-1o f-1)(x) 

If so then you could have just done this:

(fog)-1(3) = (g-1o f-1)(3) = g-1( f-1(3) ) = g-1(2) = 5

Edwin