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Transformations, Algebra Trouble

  1. Jun 4, 2009 #1
    1. The problem statement, all variables and given/known data If f(x)=[tex]\frac{2x+1}{x+2}[/tex], the equation for y=f^-1(x) is?
    So I switch x, x=[tex]\frac{2y+1}{y+2}[/tex]

    3. The attempt at a solution
    I've tried many ways, but I must be going wrong somewhere, here's what I think to be my nearest:
    x(y+2)=2y+1
    x(y)+2x=2y+1
    x(y)+2x-2x=2y+1-2x
    x(y)=2y+1-2x
    x(y)-2y=1-2x
    And that's as far as I get, it seems I'm stuck in an endless x loop or it simplifies too much to get the correct answer, so I must be missing a vital step or rule.
    Sorry, it has been a while since I've done this, and I'm not quite sure if I am even attempting it right. Any tip would be very helpful, I think the answer is:
    y=[tex]\frac{1-2x}{x-2}[/tex]

    Thank you.
     
  2. jcsd
  3. Jun 4, 2009 #2

    Cyosis

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    Homework Helper

    The answer is correct.

    y(x-2)=1-2x
     
  4. Jun 4, 2009 #3
    Interesting. Let me see if I understand.

    x(y)-2y=1-2x <----Am I to factor(not sure if that's the proper word) the left side to get that final answer then, similar to what you showed?

    And then I get y(x-2) after the factor
    Which then is y(x-2)=1-2x
    And then I can get my final answer of:
    y=[tex]\frac{1-2x}{x-2}[/tex]

    So that is all I was missing? Then it makes sense now. Thank you very much!
     
  5. Jun 4, 2009 #4

    Cyosis

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    Yep just factor and then divide by x-2 on both sides.
     
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