SOLUTION: Give the domain f(x)= x^4+4/x^2+6x-16 Answer shows (-∞,-8)u(-8,2)u(2,∞) I am coming up with (-∞,-8)u(2,∞) Which is correct and why? Thank you

Algebra ->  Rational-functions -> SOLUTION: Give the domain f(x)= x^4+4/x^2+6x-16 Answer shows (-∞,-8)u(-8,2)u(2,∞) I am coming up with (-∞,-8)u(2,∞) Which is correct and why? Thank you      Log On


   

Question 220158: Give the domain
f(x)= x^4+4/x^2+6x-16
Answer shows (-∞,-8)u(-8,2)u(2,∞)
I am coming up with (-∞,-8)u(2,∞)
Which is correct and why?
Thank you
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+%28x%5E4%2B4%29%2F%28x%5E2%2B6x-16%29
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They are right.
Here's why.
Your domain is all real values of x EXCEPT x = -8 and x = 2
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(-infinity,8) covers the interval from minus infinity < x < -8.
(2,infinity) covers the interval from 2 < x < infinity.
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you are missing the interval from -8 < x < 2 represented by:
(-8,2)
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number line would show that as follows:
-infinity-----------------------(-8)---------------------(2)----------------infinity

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Give the domain
f(x)= x^4+4/x^2+6x-16
Factor where you can:
f(x)=[x^4+4]/[(x+8)(x-2)]
Comment: Only x=-8 and x=2 are
excluded from the domain. Your
answer does not include the values
of "x" between -8 and 2.
The book's answer covers all Real
Numbers except x=-8 and x=2, which
is the correct answer.
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Cheers,
Stan H.
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