Question

h(x)=underroot3x-12 find the domain

Answer 1

\[ h(x)= \sqrt{3x-12} \]

So the previous problem was: NO DIVIDE BY ZERO.

this one is : NO SQUARE ROOTS OF A NEGATIVE NUMBER

Answer 2

the "bad x's" will make 3x-12 < 0

Answer 3

greater thn 0? how

Answer 4

less then i mean

Answer 5

You need to solve relations:
3x-12 < 0

Have you seen problems like this (but never learned) or you never saw it before?

Answer 6

never seen i guess

Answer 7

could you find x if it were an equation
3x-12 = 0

Answer 8

x=4

Answer 9

if you change the = to < that is the answer
x< 4

relations are almost the same as equations EXCEPT IF YOU DIVIDE BY A NEGATIVE NUMBER

Answer 10

so to find the good x's we want
3x-12>0
can you solve this?

Answer 11

x>4

Answer 12

that is your domain (all good x's)

Answer 13

so x>4 which means x not equal to 0

Answer 14

wait. we want
3x-12≥ 0
x ≥=4
because x=4 is allowed.

Answer 15

hmm

Answer 16

getting it now

Answer 17

what abut the under root?

Answer 18

x≥4 means x greater than or equal to 4

numbers like 4, 4.1, 5, 5.3444 , 37, etc, etc...

Answer 19

so my answer is x/x>4 .

Answer 20

You have found all the x's that give a 0 or positive number under the root, so f(x) will have a valid number.

All the numbers that f(x) can be is the RANGE of f(x)

Answer 21

I need to find the x and then write it in set builder notation

Answer 22

almost: X where X≥4 (X>4 would exclude 4, but 4 is ok... try it)

Answer 23

and the number is 4 we found out by calculating the equation.

Answer 24

\[ \{ x | x\in R, x≥4 \} \]

Answer 25

and the number is 4 we found out by calculating the equation.
we found 4 by insisting that
4x-12 ≥ 0 (the stuff inside the root must not be negative)

Answer 26

and what we did with the sq root?

Answer 27

ok Now I am getting the concept

Answer 28

The question was
find the domain

that means what are all the good x's ?
square root is used to find f(x), not the good x's

Answer 29

ok

Answer 30

here is the next situation in next question

Answer 31

if it is 4 / under root x-9?

Answer 32

looks like we have to use both rules: NO DIVIDE BY ZERO, NO SQUARE ROOTS OF NEGATIVE NUMBERS

\[ f(x)=\frac{4}{\sqrt{x-9}} \]

can you write the relation for all "good x's"?

Answer 33

x=4/9

Answer 34

x/x>4/9

Answer 35

you want to look just at the stuff under the root. It must be positive.
x>4/9 would mean 1 should be good. (1 is bigger than 4/9, right?)
by 1-9 is -8, and no negatives allowed inside the square root.

so just look at x-9

Answer 36

x/x>9 onlyy and for get about 4?

Answer 37

remember what you are looking for: negatives inside the root. the 4 up top won't affect anything. also, make sure you do not get 0:
Let's check
if x were 9 the bottom would be sqrt(0) =0 BAD. so x>9 is the answer.

Answer 38

and if under root t-4/3t-21. so in this case we will look only on the top under root one>

Answer 39

?

Answer 40

and for get the bottom one?

Answer 41

better post that. It is complicated.

Answer 42

ok