Find the domain of the function $$f(x) = \frac{1}{x+8} + \frac{1}{\sqrt{x - 8}} + \frac{1}{\sqrt{8 - x}}.$$ Express your answer as a union of intervals.
There is no domain
The first function has a domain of (-8, inf)
The second function has a domain of (8, inf)
The third function has a domain of ( -inf, 8)
No real number satisifies all three intervals