# Thread: A better way to do Maximal Domains?

1. ## A better way to do Maximal Domains?

Hello,
When finding the maximal domains of equations I have always used a basic trial and error (guessing perhaps) method of finding the right numbers, but this takes time. I was wondering if anyone knows a quicker way to do this because i have exams coming up in a week or two and trial and error (or at least how i'm doing it) takes to much time especially in an exam.

For example, (x^2 + 2) / (x^2 - 2)

Is there a soultion that makes these and other domain questions easier then simply trial and error?

Thanks

2. Originally Posted by Kaynight
Hello,
When finding the maximal domains of equations I have always used a basic trial and error (guessing perhaps) method of finding the right numbers, but this takes time. I was wondering if anyone knows a quicker way to do this because i have exams coming up in a week or two and trial and error (or at least how i'm doing it) takes to much time especially in an exam.

For example, (x^2 + 2) / (x^2 - 2)

Is there a soultion that makes these and other domain questions easier then simply trial and error?

Thanks
Yes, its not too hard. Just assume that for startes the domain is $\displaystyle \forall{x}\in\mathbb{R}$

Then narrow it down from there, going from problem spot to problem spot

For example we cannot have divsion by zero, we cannot have negative roots, etc.

From there it is fairly simple

So in your problem, the only forseeable discontinuity would be where the denominator equals zero.

So your domain would be

$\displaystyle \forall{x}\in\mathbb{R}\wedge{x^2-2}\ne{0}$

3. Originally Posted by Mathstud28
Yes, its not too hard. Just assume that for startes the domain is $\displaystyle \forall{x}\in\mathbb{R}$

Then narrow it down from there, going from problem spot to problem spot

For example we cannot have divsion by zero, we cannot have negative roots, etc.

From there it is fairly simple

So in your problem, the only forseeable discontinuity would be where the denominator equals zero.

So your domain would be

$\displaystyle \forall{x}\in\mathbb{R}\wedge{x^2-2}\ne{0}$

Oh ok I see, yeah that makes much more sense then what I was doing.
Thanks very much for the help