Question

(f/g) (x)=? I know the answer is (8x+32)/(3x-21).
but what is the domain? isnt it (-infinity , 7) U (7 , +infinity)? I wrote that but it is wrong...

Answer 1

The domain looks right to me.

Answer 2

but it is wrong... I dont know why......

Answer 3

Is this an online question or a textbook question?

Answer 4

Yea it is a online question

Answer 5

Try putting infinity instead of +infinity.

Answer 6

Same...

Answer 7

Sometimes online software gets thrown off if the result is not exactly as it expects it to be. Get rid of the extra space before the comma in (-infinity ,7) and in (7 ,infinity).

Answer 8

um.... Yea.. I have try that for several times like (-infinity,7)U(7,infinity),(-infinity, 7) and in (7 ,infinity)...etc but they r all incorrect... maybe i should go asking my professor...

Answer 9

But in the last one I still see the extra space in the third line from the end.

Answer 10

Yea i mean i try several ways....
it said "You have attempted this problem 24 times. " lol

Answer 11

But you have the correct answer right from the first attempt. You just may have to ask your teacher why it keeps saying it is wrong. The only x value that is not allowed is x = 7. So the domain is all values of x except 7 and that is exactly what you have stated.

Answer 12

If you find out the answer do post it. I am curious to know what your teacher has to say.

Answer 13

OK haha thx anyway

Answer 14

you are welcome.

Answer 15

he said,
"You have to find for what value x does
3/(x+4)=7

That way, the denominator you initially started with when you first plugged g in f is zero"

Answer 16

But that was NOT the question posted here.

The question was: What is the domain of (8x+32) / (3x-21) ?

Answer 17

Yea.. the full question is " Given that f(x)=[ 8/(x−7)] and g(x)=[ 3/(x + 4)], find (d) (f/g) (x)=____, and its domain is_____"

Answer 18

so maybe we have to use that equation?

Answer 19

Oh, OK. The first thing we notice is g(x) is undefined when x = -4 and f(x) is undefined when x = 7
Also when finding f/g you are dividing something by g. Whenever dividing anything you will have to first make sure you are NOT dividing by zero.

Answer 20

so.. i solve that x = -25/7...

Answer 21

How did you get that?

Answer 22

He said I have to find for what value x does 3/(x+4)=7
so 3=7(x+4)=7x+28 so x is equal to -25/7?

Answer 23

omg my professor just said "Whoops disregard that message. I though it was f of g of x."
"But it's similar. So you have to start with putting f/g. Before simplifying, what values of x male zeros on the bottom?"

Answer 24

But you would do that if we have to find f(g(x)).

f(x) = 8/(x - 7) and x cannot be 7

So to find f(g(x)) we have to make sure g(x) is not 7
So for what value does g(x) = 7?
At x = -25/7

But for dividing f/g(x) I am not sure why we need to do that.

Answer 25

um...

Answer 26

OH!!!! I FINALLY FOUND THE ANSWER!!!
Its (-infinity , -4)U(-4, 7)U(7, infinity).

Answer 27

Exactly! Look at my answer about 8 replies before.

f(x) is not defined for x = -4 and g(x) is not defined for x = 7

So (-infinity, -4) U (-4, 7) U (7, infinity)

If the original f(x) and g(x) were given in the problem this is what we would have arrived at.

Answer 28

switch f and g in line 2 above.

Answer 29

Yea.. I finally know we should find the domain before simplified.

Answer 30

Exactly! That is the moral of the story.

Answer 31

haha thx!!!

Answer 32

BTW, the answer is good for all operations involving f and g. Addition, subtraction, multiplication, division, etc. Because for one function x = -4 is not allowed and for the other x = 7 allowed. So these two numbers have to be excluded when these two functions are combined in any fashion.