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Homework Help: Finding the inverse

  1. Aug 17, 2009 #1
    1. The problem statement, all variables and given/known data
    I need to pass a test to get into college calculus, but there's a few things I've forgotten since may, one of them being how to find the inverse of a function with x in the denominator. I think I remember it being something really simple that I'm overlooking, but here it goes:

    2. Relevant equations
    f(x) = (x + 2)/(3x + 5)

    1) y = (x + 2)/(3x + 5)
    2) x = (y + 2)/(3y + 5)
    3) this is where it starts to go crazy.

    3. The attempt at a solution
    My attempts were kind of convulsive, but I hope it'll suffice to say that I know to switch y with x, then solve the problem for y, which will be the inverse. I just don't know how to get y out of the denominator without getting a really complicated answer. (edit: I put what I was saying into math form above)

    Thanks, if anyone knows this. I've done some re-learning in the past week or so; there are just a few things left that are too specific to find online.
  2. jcsd
  3. Aug 17, 2009 #2


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    Homework Helper
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    Gold Member

    Your goal is to use properties of equality of real numbers to find a formula for y. Either you can find a result or you cannot. Can you obtain an inverse in that general manner?
    In fact, a result is possible; whether the result is a function, I leave for you to decide.
  4. Aug 17, 2009 #3
    If the [tex]y=\frac{x + 2}{3x + 5}[/tex] then x+2=y(3x+5). Your goal is to present x in terms of y. Now can you proceed?
  5. Aug 17, 2009 #4
    That's where I get, but I can't go further without jumbling the whole thing up.
  6. Aug 17, 2009 #5
    Distribute the y on the right hand side, separate y and non-y terms to opposite sides, factor out y and divide.

  7. Aug 17, 2009 #6

    I can't believe I forgot simple algebra. Thanks.
  8. Aug 19, 2009 #7
    What I did was, multiply the numerator and then expand everything. Bring all the x-terms and the xy-terms to one side, and the y-terms and constants to the other. Then I factored out x, and divided by the other stuff!
    Good luck =)
    Last edited: Aug 19, 2009
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