SOLUTION: what is the domain of ? f(x)=(x-2/x^2-4 ) (i've substituted parentheses for the square root symbol. just to clarify, the whole function is square rooted. thanks!)

Algebra ->  Square-cubic-other-roots -> SOLUTION: what is the domain of ? f(x)=(x-2/x^2-4 ) (i've substituted parentheses for the square root symbol. just to clarify, the whole function is square rooted. thanks!)      Log On


   

Question 831698: what is the domain of ?
f(x)=(x-2/x^2-4 )
(i've substituted parentheses for the square root symbol. just to clarify, the whole function is square rooted. thanks!)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look for values where the function is not defined.
Example : When the denominator goes to zero, when the argument of a square root becomes negative.
In this case, you have a removable discontinuity because of the numerator.
f%28x%29=sqrt%28%28x-2%29%2F%28x%5E2-4%29%29
f%28x%29=sqrt%28%28x-2%29%2F%28%28x%2B2%29%28x-2%29%29%29
f%28x%29=sqrt%281%2F%28x%2B2%29%29
So then,
x%5E2-4=0
x%2B2=0
x=-2
Additionally,
1%2F%28x%2B2%29%3E0
x%2B2%3E0
x%3E-2
So the domain is x%3E-2
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28%28x-2%29%2F%28x%5E2-4%29%29%29+