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Homework Help: Inverse of function and its domain/range?

  1. May 30, 2010 #1
    1. The problem statement, all variables and given/known data

    a) find the inverse of f(x)= (3x+4)/(5-2x)
    b) state the domain anr rage for both f and f^-1


    2. Relevant equations



    3. The attempt at a solution

    for f(x)
    Domain:x ≠ 5/2, x ∈ R
    Range: y ≠ 3/2, y ∈ R

    Inverse (my answer):

    f^-1(x) = (5y-4)/(3+2y)

    I want to check and see if this is correct, and also get some guidance of the domain/range for the inverse?

    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 31, 2010 #2
    how did you get that 3/2 is not in the range?

    what about f(0.5833333333)?

    f^-1 looks right though.
     
    Last edited: May 31, 2010
  4. May 31, 2010 #3
    I evaluated the limit from x > inf and a > -inf


    When you do that, the result becomes -3/2

    (sorry, just realized it wasnt -'ive above. Should be -3/2!)
     
  5. May 31, 2010 #4
    but shouldn't that be missing from the domain of f^-1 ?
    The range of f is all of R and the range of f^-1 is also all of R

    right?
     
  6. May 31, 2010 #5
    What ive put above is just the domain and range for f(x)

    Domain:x ≠ 5/2, x ∈ R
    Range: y ≠ -3/2, y ∈ R

    --------------------------------------------------------

    Its the inverse, f^-1(x), that I need help finding the domain and range for now.
     
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