Question

Determine the natural domain of the function

Answer 1

\[f(x)=\frac{ \sqrt{(x ^{2-4)(x+4)}} }{ x-5 }\]

Answer 2

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,∞)

Answer 3

ummm is it maybe
\[f(x) = \frac{\sqrt{(x^{2}-4)(x+4)}}{x-5}\]
like this?

Answer 4

oh yeah. sorry about that.

Answer 5

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...

Answer 6

@pgpilot326 wait, is the answer 3. ?

Answer 7

remember, x can't be 5 because we'd be dividing by 0 and that's not allowed!

Answer 8

you there?

Answer 9

yes yes! your answer was right! thank you so much!

Answer 10

it's not about the answer but the method...