Interval notation of function's domain question

[late347]

Homework Statement

find domain
f(x)= ## \frac{\sqrt{x^2-x-6}}{x-5} ##

Homework Equations

The Attempt at a Solution

[/B]
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}

 

[member 587159]

Homework Statement

find domain
f(x)= ## \frac{\sqrt{x^2-x-6}}{x-5} ##

Homework Equations

The Attempt at a Solution

[/B]
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}

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

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