Radical Function Problem

leapfrog

New member
Joined
Sep 1, 2013
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2
Hi,

I've been struggling to find the domain of the problem: f(x) = sqrt (-x - 3) / (x^2 + 5x - 6). For clarification, only the numerator has a square root under it. I factored out the denominator, and came up with 1 and -6 needing to be omitted. I worked out the numerator, and got x ≤ -3. So, I typed in the following (this is for a web assignment): (-∞, -6)U[-3, 1)U(1, ∞). This turned out to be incorrect, and I'm currently stumped on what, exactly, I'm not doing correctly. For all I know, I may have done the entire problem wrong.
 
As long as you got x ≤ -3, the domain cannot be (-∞, -6)U[-3, 1)U(1, ∞), because that includes also the values of x>-3.
So, it must be (-∞, -6)U(-6, -3].
 
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