Posted by sh on .
What's the domain of √((x-2)/(x^2+x-6))
The proposed answer is good for √(x-2).
However, since the denominator becomes negative between -2 and 1, the expression in the square-root radical is therefore positive on this interval.
So the domain can be revised to [2,∞)∪(-2,1).
Note that +2 is within the domain, because the denominator becomes zero. However, -2 and 1 are excluded because the denominator becomes zero.
When I factor out the bottom its x=-3 and x=2, how did you get -2 and 1? Why is +2 included? Doesn't it become undefined when x=2?