Question

p(t)=under root t-4/3t-21 find the domain

Answer 1

the first one is the correct one

Answer 2

he unde root is just on the top

Answer 3

the under root is just on the top

Answer 4

\[p(t)= \frac{ \sqrt{t-4} }{ 3(t-7) }\]

Answer 5

yes

Answer 6

First, let's do the no divide by zero. What bad t do we exclude?

Answer 7

the one on the top

Answer 8

?

Answer 9

You have a fraction. If the bottom is zero, that is bad. what t must we not allow?
(otherwise we will divide by 0)

Answer 10

so on the top t>4

Answer 11

so on the top t>4
ALMOST. t >= 4 RIGHT?

Answer 12

sqrt(0) is 0 that is ok (it is defined)

Answer 13

now find the bad t that makes the bottom zero.

Answer 14

yes right and what abut 3 and 7?

Answer 15

that is 7 and 3

Answer 16

bad one which makes t 0

Answer 17

or just -7

Answer 18

to find the bad t:
solve
3(t-7)=0

Answer 19

divide by 3
add 7

Answer 20

3 divided by 7?

Answer 21

3(t-7)=0 divide both sides by 3
(t-7)= 0/3 or
t-7=0

can you finish?

Answer 22

t=-7

Answer 23

I mean t=7

Answer 24

I guess not!

Answer 25

t=7, much better.

so you have
all real numbers t where t>=4 and t≠7
as the domain.

Answer 26

why t is not equal to 7?

Answer 27

why not t>7 .

Answer 28

The t=7 makes the bottom 0. NO DIVIDE BY ZERO.

Answer 29

For the top to be ok t must be 4 or bigger. But when you get to 7, you have to toss it, because the bottom becomes 0 when t=7.

Answer 30

ok

Answer 31

is that a ok (I don't get it) or an
ok (I understand)
?

Answer 32

hm well I still did not get how t=7 is not equal to 7:(

Answer 33

I did got the concept of how to find the domain. How to find the good and bad x .

Answer 34

I also learnt tht we have to simplfy and then see if x> any number.

Answer 35

The domain is all the "good t's"

when you found t=7 makes the denominator 0, you found a "bad t"
so you take the good t's from the top, and then say, by the way, don't include this bad t. You say t ≠7 (read this as "t is not allowed to be 7")

Answer 36

ohhhh . I was looking it from another angle. I was thinkinh of the 4 on the top..

Answer 37

t=7/0 not ok

Answer 38

right?

Answer 39

Let's simplify this: what is the domain for
f(x)= 1/(x-7) ?

It is all real numbers , except 7
you say x is all real numbers, x≠7

For this problem, it is almost the same, except
x is all real numbers ≥ 4, except for 7

x is all real numbers ≥4, x≠7

Answer 40

where the 4 came?

Answer 41

you have
\[ \sqrt{t-4} \]
in the numerator. You want the stuff inside the root to be 0 or positive. (no negatives)

so you want
t-4≥0 or
t ≥4

Answer 42

ok yes this part is under stood.

Answer 43

I am really worried how will I pass this class?

Answer 44

You seem to be learning it.
I'll be back tomorrow about the same time. Meanwhile others will help you.

Answer 45

thanx alot. I wil take a break too.