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Pre calc review - interval notation

  1. Aug 26, 2014 #1
    1. The problem statement, all variables and given/known data
    What's the domain of 14/x2-x-6, in interval notation?


    2. Relevant equations

    [itex]\underline{14}[/itex]x2-x-6

    3. The attempt at a solution
    [3, + infinity)
    [-2,- infinity)
    Sorry, I can't find the infinity symbol

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



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 26, 2014 #2

    Ray Vickson

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    You wrote
    [tex] \frac{14}{x^2} -x-6 [/tex]
    when read using standard rules for parsing mathematical expressions. Did you really mean that, or did you want
    [tex] \frac{14}{x^2 - x - 6} \: ?[/tex]
    If you meant the latter you absolutely MUST use parentheses, like this: 14/(x^2 - x - 6).
     
  4. Aug 26, 2014 #3
    My mistake, the denominator SHOULD be in parentheses.
     
  5. Aug 26, 2014 #4

    LCKurtz

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    What about values between 3 and -2?
     
  6. Aug 26, 2014 #5

    HallsofIvy

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    You mean 14/(x2- x- 6)= 14/((x- 3)(x+ 2))


    No, this is wrong because it does not include such numbers as x= 0 for which 14/(0- 0- 6)= -7/3 or x= -5 for which 14/(25+ 5- 6)= 7/12.

    Strictly speaking this is bad notation- it should be (-infinity, -2]. (The smaller goes on the left.)
    But even that is not correct because it does not contain x= 0 and x= 5 for which 14/(25- 5- 6)= 1.

    The correct answer is NOT a single interval, it is a union of three disjoint intervals.

     
  7. Aug 27, 2014 #6
    I'm surprised no one's mentioned the incorrect use of the square bracket to end the set.
     
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