Question

Given f(x) = x+3 and g(x) = X-6, where is the function f(x)/g(x) continuous?

Answer 1

missing a few parts i think

Answer 2

I just fixed it, sorry about that

Answer 3

recall that its illegal in all 50 states and some regions of canada, to divide by zero

Answer 4

this thing is NOT continuous at g(x) = 0

Answer 5

Do you know how to do the formulas for each of the steps of finding the continuity of a problem?

Answer 6

dunno what you mean by formulas; as is this things tells you to put the definition of g(x) under the definition of f(x); as such we get a glorified fraction that is continuous along different intervals

Answer 7

g(x) = 0 when x-6=0 ; so we exclude x=6 form the domain and get:

(-inf,6)U(6,inf)

Answer 8

A function F is continuous at c if all three of these conditions are satisfied:
1. f(c) is defined.
2. lim f(x) = f(c) exists
x->c
3. lim f(x) = f(c)
x->c
Those are the rules. I would have to use this to make sure the above equation is continuous.

Answer 9

well, if F = f/g ; then the only hangup we have is at x=6

F(6) is not defined therefore we need not move on unless your a glutton for punishment :)

Answer 10

The reason I am not getting it is because the answer says: The function f(x)/g(x) is continuous for all x except x=6. The answer is undefined (because of the zero denominator) and not continuous. So why does the answer say continuous except 6?

Answer 11

... can we divide by zero? is that a mathematical do-ability?

Answer 12

I have another problem that says state whether continuous at the indicated point. If its not continuous tell why.
g(x) = x^2-9/x-3; x=3

Answer 13

the answer for that one is not continuous, g(3) does not exist

Answer 14

\[\frac{f(x)}{g(x)}=\frac{x+3}{x-6}\]

Answer 15

tell me, what is 4/0 equal?

Answer 16

yes i understand that.

Answer 17

g(3) = 3^2-9/3-3 also makes it zero. so why is this problem not continuous and the other one is?

Answer 18

are you trying to equate g(x) from one example to g(x) in another example? g(x) is just a name that gets recycled over and over again.

Answer 19

you wrote: "The reason I am not getting it is because the answer says: The function f(x)/g(x) is continuous for all x except x=6."

Is continuous at all EXCEPT 6, therefore it is NOT continuous at x=6

"The answer is undefined (because of the zero denominator) and not continuous. So why does the answer say continuous except 6?"

EXCEPT at 6 is what you write, whch means this is NOT continuous at x=6

Answer 20

LOL ok thank you. :)

Answer 21

your just reading it alittle off :) happens to the best of us at times lol

Answer 22

yes, plus I have been studying this for a few days. I haven't done math in 10 years and now they are making me do calculus lol. Thank you again! :)

Answer 23

youre welcome, I was outta highschool 20 years before I went to college

Answer 24

WOW, proud of you! keep it up! :)