SOLUTION: Determine the natural domains of the function of x: 5/sqrt(x^2-4)

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Question 889943: Determine the natural domains of the function of x: 5/sqrt(x^2-4)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Two issues with regards to the function is when the denominator goes to zero since division by zero is undefined and when the argument for the square root is less than zero since that's also undefined.
So,
x%5E2-4%3E0
Two boundary points are x=-2 and x=2.
We can graph the denominator,
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2-4%29
We see that between x=-2 and x=2 inclusively, the argument for the square root would be negative or zero.
So the domain is,
(-infinity,-2)U(2,infinity)