SOLUTION: Square root of x+14 over x-5 find the domain in interval form

Question 841658: Square root of x+14 over x-5 find the domain in interval form
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
When looking for domain, look for two main things. 1. There can't be a - number under a square root. 2. There can't be a 0 in the denominator.

x+14 is under the square root, so x+14 must be >= to 0

x+14 = 0

x=-14. Set up intervals, and test a number within each interval.

Intervals are -infinity to -14 to infinity. A number in the first interval is -20. -20 + 14 >=0? No.

-14 + 14 >= 0 is true, so -14 is included.
A number in the second interval is 0. 0+14 >= 0? Yes. So the interval for the domain is [-14,infinity).

The denominator may further limit the domain. x-5 cannot = 0

x-5=0

x=5.

x cannot be 5.

The domain is [-14,5) U (5,inf)

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