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Homework Help: Composition of Functions help please!

  1. Apr 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Find g(x) if f(x) = (3x-1)/(2x+5) and f(g(x)) = (x+9)/(12x-11)

    2. Relevant equations
    N/A, as far as I know

    3. The attempt at a solution

    I tried doing it as though g(x) = y and it turned out like this:
    (3y-1)/(2y+5)=(x+9)/(12x-11)
    I very quickly saw that that wouldn't work though, so I'm kind of lost. This is independent work in order for me to be able to go into pre-calc, so while I can ask a teacher it is difficult to find time, hence why I'm relying on you guys :) Help would be much appreciated!
     
  2. jcsd
  3. Apr 12, 2012 #2
    Think about it like this: you have f(x), and you have f(x) in the specific case when x=g(x), what you are looking for is what does x have to be in f(x) to give f(g(x)).

    So, what does x have to be exchanged with in (3x-1)/(2x+5) to give (x+9)/(12x-11)
     
  4. Apr 12, 2012 #3
    Well, I already got that part of the logic which is why I set g(x) equal to y, but it didn't work, so I don't understand how to get it to work.
     
  5. Apr 12, 2012 #4
    Maybe you can find [itex]f^{-1}(y)[/itex]??

    That is, set

    [tex]y=\frac{3x-1}{2x+5}[/tex]

    and try to find x in function of y.
     
  6. Apr 12, 2012 #5
    Ok, I just went through the math and its a bit of a long haul. Should be fairly easy but its tedious.

    What you want to do is take your f(x) function, replace x with g(x), set it equal to your f(g(x)) function and then solve for g(x).
     
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