anonymous
  • anonymous
Determine the natural domain of the function
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[f(x)=\frac{ \sqrt{(x ^{2-4)(x+4)}} }{ x-5 }\]
anonymous
  • anonymous
express the answer in interval notation. here are the answer choices: 1. (−∞, −4]∪[−2, 5)∪(5, ∞) 2. [−4, −2]∪[2, 5)∪(5, ∞) 3. (−∞, −4]∪[−2, ∞) 4. (−∞, −5)∪(−5, −2]∪(2,∞) 5. [−4, −2]∪[2, ∞) 6. (−4, 5)∪(5,∞)
anonymous
  • anonymous
ummm is it maybe \[f(x) = \frac{\sqrt{(x^{2}-4)(x+4)}}{x-5}\] like this?

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anonymous
  • anonymous
oh yeah. sorry about that.
anonymous
  • anonymous
okay... so first off we can't divide by 0, right? so that excludes a particular value of x. next, whatever is under the square root must be >=0. so set the inside of the root >= 0 and find all the values of x that make it 0. then set up a number line and mark those values on it. next evaluate in each section created by those values to see if the function will be positive or negative. it seems a bit wordy but find the zeros and i"ll draw a pic for you to see...
anonymous
  • anonymous
@pgpilot326 wait, is the answer 3. ?
anonymous
  • anonymous
|dw:1378442603082:dw|
anonymous
  • anonymous
remember, x can't be 5 because we'd be dividing by 0 and that's not allowed!
anonymous
  • anonymous
you there?
anonymous
  • anonymous
yes yes! your answer was right! thank you so much!
anonymous
  • anonymous
it's not about the answer but the method...

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