Set Builder Notation

  1. Hi!

    We have 3 functions; f=[​IMG], g=[tex]\frac{1}{\sqrt{(2x2 - 1)(x2-1)}}[/tex] and h= [tex]\frac{\sqrt{2+x}+x(x^2-1)}{(x^2-1).\sqrt{2+x}}[/tex]

    And we want to write the domain of these functions in the set builder notation, which I'm not very familiar with.

    Well, I know that for the Domain of g, x ≠ 0 and ±1. How do we write it in that notation? is it [0,∞]\{±1}?

    For the domain of f, x must be greater than or equal to -2 and it cannot equal 0 & ±1

    In h, domain: x≥-2, & it can't be ±1 as well.


    I need to write the domains of these functions in the set builder notation. Not knowing something doesn't mean you're stupid, just asking about it ... :biggrin:

     
  2. jcsd
  3. nicksauce

    nicksauce 1,275
    Science Advisor
    Homework Helper

    You could write the domain of x as [-2,∞)\{0,±1}
    or as
    Dom(f) = {x |x [itex]\in[/itex] [-2,∞)\{0,±1}}

    Make sense?

    Notice the open parentheses on the infinity, since x cannot actually infinity (as it is not a number)
     
  4. OK, Nick. How should I express the domains of g and h?

    Where g = [tex]\frac{1}{\sqrt{(2x^2 - 1)(x^2-1)}}[/tex]

    Would the domain of g be written as: dom(g)= R\{0, ±1} ?


    And... how would the domain of h be in this notation?
     
    Last edited: Jul 30, 2008
  5. nicksauce

    nicksauce 1,275
    Science Advisor
    Homework Helper

    Yes that would be a way to write the domain of g.

    For h you could write
    Dom(h) = [-2,∞)\{±1}
     
  6. Right :wink:
    Thanks a lot! Makes sense now...
     
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