# Interval notation of function's domain question

1. Feb 26, 2017

### late347

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. Feb 26, 2017

### Math_QED

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

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