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Homework Help: Find out domain and range

  1. Jun 24, 2008 #1
    1. The problem statement, all variables and given/known data

    y = [tex]\frac{1}{(x-1)(x+2)}[/tex]

    find out the domain and range

    ans: y<= -4/9 or y>0

    [tex]x~E~R~-\{-2,1\}[/tex]





    3. The attempt at a solution

    I know the solution and I used this methoD:

    y(x^2 + x -2) =1 (where [tex]y\neq0[/tex] )

    when x is real, the discriminant

    y^2 -4y(-2y-1) >=0 (where [tex]y\neq0[/tex] )

    9y^2 + 4y >= 0 (where [tex]y\neq0[/tex] )

    y(9y +4) >= 0 (where [tex]y\neq0[/tex] )

    y<= -4/9 or y>0


    My request is ... plz use some other easy method to illustrate this problem.. I want to know other methods of solving this same problem.. plz help.

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    Forum $ignature: www.lingouist.blogspot.com[/URL]
     
    Last edited by a moderator: Apr 23, 2017
  2. jcsd
  3. Jun 24, 2008 #2
    This is the simplest way that I know of. If graphing is simple enough, you can try.
     
  4. Jun 24, 2008 #3

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi sinjan.j! Welcome to PF! :smile:

    Easy method:

    It looks nearly symmetric …

    so adjust it to make it symmetric! :smile:

    Hint: the range will be the same even if you make a substitution for x. Try w = x - a, where you choose a to make 1/(x-1)(x+2) symmetric in w.
     
  5. Jun 24, 2008 #4
    simpler method = calculator
     
  6. Jun 24, 2008 #5
    Thanx everbody

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    Forum $ignature: www.lingouist.blogspot.com[/URL]
     
    Last edited by a moderator: Apr 23, 2017
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