Question

Which statement describes the domain of the function \[F(x)=\frac{ 3x }{ 4x-4 }\]?
all real numbers
all nonzero real numbers
all real numbers except x = \[\frac{ 3 }{ 4 }\]
all real numbers except x = –1 and x = 1

Answer 1

@mathmale

Answer 2

First, please tell me what you know about the word / concept, "domain." That's of critical importance here.

secondly, you may find this question easier to answer if you re-write it as\[F(x)=\frac{ 3x }{ 4(x-1) }\]

Answer 3

i really dont know much about the domain in this concept

Answer 4

I'll then have to give you some tough love by asking you to look up "domain" now. No sense in trying to find something when you're unsure of what the concept means. Have you a textbook, or online materials, to read and study? Has your teacher discussed examples of finding the domain of a function?

Answer 5

I'll give you one of my versions of the meaning of "domain:" it's the SET of input (x-) values for which your function IS DEFINED.

Answer 6

i totally messed uo on the quetion its suppose to be \[\frac{ 3x }{ 4x ^{2}-4 }\]

Answer 7

sINCE division by zero is not defined, the domain of the function in question does not include x=1. Why is that? Because you'd have zero in your denominator if x=1. NO WAY.
so you could write the domain (the set of ACCEPTABLE input values in one of several ways:

"x is not equal to 1"

(-infinity, 1) U (1, infinity)

Answer 8

If your function is:\[F(x)=\frac{ 3x }{ 4x-4 }\]... do the same thing as before: factor the denominator, set the resulting expression = to 0, and solve for x, to find values of x that are NOT part of your domain.

Answer 9

\[F(x)=\frac{ 3x }{ 4x^2-4 }=F(x)=\frac{ 3x }{ 4(x^2-1) }=?\]

Answer 10

so the answer would be the last option right

Answer 11

Note: You can, and must, factor this denominator further. Once done, set the resulting string of factors = to 0 and solve for x. You should obtain 2 values.

Sorry, bre, but I just do not deal in yes or no answers. Instead, I'd like for you to show or explain to me in words how you got your own answer.

Answer 12

By the time you've done that, you'll be able to choose the correct answer with confidence, by yourself.

Answer 13

What are the roots / zeros of x^2-1=0?

Answer 14

x would equal 1 or -1 if i were to simplify the numerator further right

Answer 15

Yes, that's correct; you correctly factored x^2-1 into (x-1)(x+1), and then you let (x-1)(x+1)=0, obtaining roots +1 and -1. Very good!

Is this the domain? Think carefully!

Answer 16

no? becuase if i were to plug 1 or -1 to x it would equal to zero and that cant happen?

Answer 17

so would my answer be all real number except 1 and -1