Question

How can I find the domain of the function g(x) = x / x^2 - 1 ?

Answer 1

without a graph

Answer 2

Usually, in domain problems, you get expressions in radicals or in denominators.
In your case, you have a denominator x^2 - 1

In these cases, the domain is all real numbers EXCEPT those that would make your denominator zero.

When is your denominator zero?

Answer 3

when is 1

Answer 4

the value of x

Answer 5

Yes... and there's another.
Indeed, if x = 1
x^2 - 1 = 0

What else?

Answer 6

and -1 ? :D

Answer 7

That's right :)
And those are the only ones...
x^2 - 1 = (x+1)(x-1) = 0
So, your domain is all real numbers EXCEPT those that would make your denominator zero, which are 1 and -1

Good job :D

Answer 8

can it be expressed as [X|X <> -1,1] ?

Answer 9

I prefer R - {-1 , 1}
No, it can't be expressed like that because numbers BETWEEN -1 and 1 are still in the domain.

Answer 10

hmm here the answer is demostrated as {X|X <> -1,1} but I dont know why

Answer 11

For one thing, I don't know what that notation means :(

Answer 12

I think <> is another way to say ≠

Answer 13

yes its ≠

Answer 14

Well, if that's the case, then go for it, it's correct :)

Answer 15

but why ? :D you said the numbers between are still in the domain?

Answer 16

Yeah, they are, but if what you say is true, that <> is the same as writing ≠
then the set
{X|X <> -1,1}
is correct because it is read as
"the set of all x such that x is not equal to -1 or 1"
Which does not exclude numbers between -1 and 1 :)

Answer 17

Would it be easy for you to explain to me the meaning of | between those 2 x ? It's the first time I am seeing such a notation

Answer 18

Okay, that's what you call the rule method of listing sets, I think...
Takes this form:
{x | x <bla bla bla>}
I'll take you through it part-by-part
{x
(the set of all x)
|
(such that)
x <bla bla bla> }
(x fulfills some sort of condition)

For example, the set of all even integers may be denoted as
{x | x is an integer, x = 2k, for some integer k}

Answer 19

By the way, it need not be just one parameter (x).
For instance, the set of all complex numbers may be denoted as
{a+bi | a and b are real numbers, i is the square root of negative 1}

Answer 20

Can you help me translate {X|X ≠ -1,1} into words?