Question

Find the domain of function:

h(x)=√(x-4)/(x^2-x-12)

Answer 1

So the domain is all of the values that x can be that will result in a solution in a way right?
So right off the bat anything at would make this negative is a no no but more importantly what would make this undefined?

Answer 2

If i break apart the denominator i get (x-4)(x-3) if I plug in 4 or 3 i will get no solution so those cannot be included in the domain

Answer 3

wait is it \[\sqrt{x-4}/(x ^{2}-x-12) or \sqrt{(x-4)/(x ^{2}-x-12)}\]

Answer 4

its the first one?

Answer 5

okay perfect x has to be greater than 4!

Answer 6

sorry i kept too long

Answer 7

do you understand the entire answer?

Answer 8

so do i work for the denominator or?
and equate it to 0

Answer 9

yeah you set it to zero and solve for x

Answer 10

only the denominator right?

Answer 11

yeah

Answer 12

oh kk.then x=-3 and 4

Answer 13

the reason I'm saying greater than 4 is because you need absolutely need to half the top portion of the fraction greater than 0

Answer 14

yeah sorry i put 3 and 4 its -3
but -3 doesnt even work because if we put that in the top becomes undefined

Answer 15

there is no square root of negative numbers

Answer 16

so what is the answer then?

Answer 17

x>4

Answer 18

that is the answer

Answer 19

Sorry was trying not to put all the pieces together. Trying to let you figure out some of it so you can learn from it.

Answer 20

oh okay.

Answer 21

so u plugged the numbers in the denominator or the numerator

Answer 22

to see if its correct

Answer 23

hehe you should fix you're skype I could explain this much easier

Answer 24

i want to know how i can check for my anawers

Answer 25

sec let me pause my tv to explain it

Answer 26

kk

Answer 27

okay so! the point of this problem is to see when the function is undefined because that would mean that it is not in the domain. The domain meaning what numbers can I put in for x that will give me solutions.

Answer 28

so the first step in this is to look okay how can I make this undefined. we look and look we see a square root- well we know square roots cannot contain negative numbers theres your first portion to you answer so we know that x-4=0 x=4 so X can be greater than or equal to 4

Answer 29

thats the first part.

Answer 30

now the denominator- we see a function lets say F(x)=root(x-4)/y y=x^2-x-12 when y=0 the function F(x) is undefined correct?

Answer 31

undefined, correct?

Answer 32

*

Answer 33

yes

Answer 34

so we need to figure out how to make this function 0 the only way possible is by factoring so we factor it out, like you did, got x+3=0 and x-4=0 giving us x=-3,4

Answer 35

now if we combine the conditions of the first the numerator we know that we cannot have -3 in our answer as far as the domain because it is less than and not equal to 4

Answer 36

does that make sense to you?

Answer 37

so i always need to work out for the numerator first before the denominator

Answer 38

haha no im sorry my point was you need to make sure both agree with each other

Answer 39

you wont always have a square root so sometimes the top wont even matter

Answer 40

so that means after fnking x and plugging x into the equation the equation shoulb be equal to zero?

Answer 41

finding

Answer 42

on the bottom yes because that will make the overall equation undefined

Answer 43

oh okay

Answer 44

if its undefined it is not part of the domain

Answer 45

get it now?

Answer 46

didnt get what u last said.i thot the domain should be undefined

Answer 47

if you select an x that results in the function being undefined that value for x is not included in the domain

Answer 48

so 4 does work because it makes the dominator zero. so it can't be part of the domain

Answer 49

doesnt work*

Answer 50

oh so any number that doesnot equate a function to zero is undefined?

Answer 51

hmmm okay undefined is a messy word. It's essentially you've violated a golden rule like dividing by zero

Answer 52

I didnt really understand what were were saying with that last phrase

Answer 53

oh ok .so if im getting u,,since 4 plugged into the denominator makes the function =0 which is undefined 4 cannot be a domain

Answer 54

hmm okay so I probably shouldnt have used function like I did without defining all the equations as functions. if I plug in 4 it makes the dominator zero making the function undefined because we're dividing by zero.

Answer 55

let me write it out on paper and post a picture.

Answer 56

oh ok

Answer 57

the way im going to show you is a little unorthodox but i think its the best way to understand problem like this.

Answer 58

lol ok

Answer 59

still waiting..lol

Answer 60

sorry making it easy to understand

Answer 61

okayy

Answer 62

ok so the answer as i see is >4

Answer 63

yes

Answer 64

\[i was thinking the anwer was gonna be(-i\[\[i was thinking the anwer was gonna be(-\infty,-3) or (-3,4) or (4,\infty)

Answer 65

well it can be expressed as (4,inf)

Answer 66

its the same thing

Answer 67

oh ok.

Answer 68

thanks so much you soo helpful

Answer 69

no problem!

Answer 70

also

Answer 71

your other problem that i answered

Answer 72

you probably arent doing derivatives yet are you?

Answer 73

http://openstudy.com/updates/51d37bafe4b0befebdaf2658

Answer 74

no not yet

Answer 75

yeah i got that

Answer 76

ok will chat with you some other time.thanks very much.feeling sleepy.lol