SOLUTION: What are the domain and range of {{{ y =sqrt((x+4)/(x^2-5))}}}
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Algebra.Com
Question 477204: What are the domain and range of
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have to avoid a zero denominator so we start with the restriction: 
Next, note that on the interval 
, 
, but since 
on this same interval, 
on that interval. Since 
is undefined for 
, the interval must be excluded from the domain.
On the interval 
, 
and 
, hence on that interval, and the function is again undefined. Hence, exclude from the domain.
So the domain is all real numbers except real numbers in the two excluded ranges:
Domain: \ \small\ \cup \Large\ \left(\sqrt{5},\infty\right)\right}])
Since this is a positive square root and we have shown that there is a value in the domain, namely -4 that results in a zero value for the function, the range is 
John
My calculator said it, I believe it, that settles it
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