Question

find the domain of f(x)=(Sqrt x+3)/((x+8)(x-2))

Answer 1

Rules to memorize:
-You cannot divide by zero
-You cannot take the root of a negative number


What values of x will violate these rules?

Answer 2

well I think the answer I have hereis x>-3, x is not 2 is this correct?

Answer 3

Hint: You can take the root of zero

Answer 4

x is greater or equal to 0?

Answer 5

\[\sqrt{0} = 0\]

Answer 6

all real numbers than!

Answer 7

No, stop and think, you were close to the right answer before

Answer 8

I came up with x is greater or equal to 0 is this right?

Answer 9

Well test your answer, sub +2 into your equation

Answer 10

i did and got x is greater or equal to 0

Answer 11

The domain of a function is simply the values of x you can sub into an equation and acquire a real number as y

If you subbed +2 as x into your function you will violate a rule I listed in my first post

Answer 12

yea but i need to answer to verify please

Answer 13

\[f(2) = \frac{\sqrt{2+3}}{(2+8)(2-2)}\]

Answer 14

can you simplify that?

Answer 15

yea and the answer to prove my theory is..?

Answer 16

1/4

Answer 17

sorry 5/0

Answer 18

its not really a theory but I digress

Answer 19

ok well what would be the final answer?

Answer 20

it would be something hashtag 2 right?

Answer 21

I'm not here to give you the answer, I'm here to teach so I wont have to give you the answer

Answer 22

well if you found that 2 a possible value of x what does that tell you about the domain of f(x)

Answer 23

all real numbers except -8,3 and 2!

Answer 24

this is it right? just to make sure

Answer 25

is this right?

Answer 26

Look at my rules again
-You cannot divide by zero
-You cannot take the root of a negative number

Both of these rules apply directly to your problem, I recommend looking at each part of the expression and think about what x values will violate the rules I listed above. Then you will know what is in your domain and what isnt

Answer 27

I guess you can split this problem into two parts



Look at the denominator

(x + 8)(x - 2)
you know this cannot equal zero otherwise you would divide by zero which is not allowed (if you are interested why just search on youtube same for the other rule).

So,

Set

(x + 8)(x - 2) = 0

and solve for x


Next look at the numerator

\[\sqrt{x+3}\]

we have a radical, and we know we cannot take the root of a negative number. So what x values will cause us to have a negative number under the radical?

Answer 28

Follow?