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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