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Interval notation of function's domain question

  1. Feb 26, 2017 #1
    1. The problem statement, all variables and given/known data
    find domain
    f(x)= ## \frac{\sqrt{x^2-x-6}}{x-5} ##

    2. Relevant equations

    3. The attempt at a solution

    Well, one sees that x ≠5 and then we further investigate the dividend portion where the under-the-root expression ≥ 0

    We can graph the parabola, and find the zeroes. Then investigate the intervals and keep in mind also that x ≠ 5 for the original function.

    I'm interested in how is this domain described in the interval notation for domain such as with the [ ] brackets

    I confirmed by pen-and-paper results with wolfram alpha and the particular type of notation that wolfram alpha uses is as follows.

    domain: { x ∈ ℝ : x>5 or 5>x≥3 or x≤-2}
  2. jcsd
  3. Feb 26, 2017 #2


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    Domain: ##(- \infty,-2] \cup [3,5) \cup (5, +\infty)##

    Or: ##(- \infty,-2] \cup [3,+\infty) - \{5\}##
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