Question

@mathmale Hi again, I'm working out how to find f/g and it's domain. I think I got f/g but I'm confused on if it's domain is "x is NOT equal to 4" or "x is Not equal to -4". Can you explain how to get this?

Answer 1

Hi, Nicole! Happy to "see" you again.

If the domain is already given as "x is not equal to 4" or "x is not equal to -4," I could say with certainty that the composite function f/g has a denominator that is zero for x=4 or x=-4. Let's discuss this until you feel comfortable with the concepts involved.

Answer 2

Okay, this is what I have done.

Answer 3

This image helps so much!!

Answer 4

Good! (:

Answer 5

We can get the domain of f/g directly from the algebraic expression BEFORE factoring and simplification.
\[\frac{ x ^{2}-16 }{ x+4 }\]
(ob viously) has the denominator x+4. Let this x+4=0 and solve for x. THAT is the value that x can NOT have.

Answer 6

Your factoring and reduction, while done correctly, doesn't help much with finding the domain.

Answer 7

Okay, so how do I find if it will either be a -4 or +4?

Answer 8

I suspect you have a rational function whose denominator is (x+4)(x-4). Am I right?
If so, set that denominator, (x+4)(x-4), = to zero and solve for x.
One solution is x=4; the other is x=-4. Thus, the domain of that function is

Answer 9

"all real numbers other than 4 and -4"

Answer 10

or, alternatively, (-infinity,-4) U (-4, 4) U (4, +infinity).

Answer 11

I can only have one though.. It's either all but -4 or all but +4. I may not be understand though, I may be thinking about this differently and the answer is right there..

Answer 12

Back to the drawing board. If those are the two choices, then the denominator of your f/g is probably (x+4). If it is (x+4), then the domain of your f/g is "all real numbers other than -4." If it's (x-4), then the domain of your f/g is "all real numbers other than 4."

Answer 13

Okay, so if I come down to the answer x = 4 then its domain is going to be all real numbers except -4?

Answer 14

Not quite. let me re-phrase your question:

"OK, so if I have (x+4) in the denominator of my f/g, then the domain of f/g is going to be "all real numbers other than -4."

Answer 15

Note: you said, "x=4"
I said "(x+4)".

Answer 16

Oh, I didn't know they had to have the ( ) -my answers choices don't have them so I figured that they weren't needed. May I ask another simple quick yes or no question in this same post?

Answer 17

Sure, please go right ahead!

Answer 18

When factoring out an equation -Example: (5x + 2)(2x + 1)- would you have 10x + 5x + 4x + 2 or 10x^2 + 5x + 4x^2 + 2??

Answer 19

Nicole, I'm quite certain you mean, "When multiplying out a function expressed as the product of factors, such as (5x+2)(2x+1), which of the following would be the result? ... "
Answer: 10x^2+9x+2. Mind trying that again? Hint: x*x = x^2.

Answer 20

That's all I needed to know - I had x and not x^2 - And I thought "That doesn't look right" and I meant using "foil" not factoring.

Answer 21

So glad you feel good about this problem and hopefully about the last one as well. Again, I have to get off my computer (after having spent much of the day sitting in front of it), so I'll say good night and welcome you to come back again soon! Great working with you! MM

Answer 22

Goodnight! Thank you!

Answer 23

Bye, Nicole!