# Thread: Find the domain of each function

1. ## [solved] Find the domain of each function

Book's kind of skimpy on this

Find the domain of each function.

f(x) = x / 3x - 1

another one

f(x) = 5x + 4 / x^2 + 3x + 2

From how the book explains it, the only way I know to solve these is to plug random numbers in and see, but that's not exactly practical.

Thank you for any help.

2. Hi

A fraction is defined wherever the denominator is not equal to 0
For the first one 3x-1=0 for x=1/3
Therefore the domain is IR\{1/3}

3. Thank you,

I can see that x = 1/3 would make the denominator 0. Now that you point it out, it seems pretty obvious. However, how would I find that in problems where it's not so obvious?

4. Let me clarify what I mean. Basically, I want to know how I can systematically work out the domain without just guessing what wouldn't work.

It can be inferred just by looking at the first problem that the demoninator will be 0 if x = 1/3, but I really don't know what to do with the next problem. Is there something obvious I'm missing? Could someone work out the next problem, step-by-step?

Maybe the next problem IS obvious just by looking to most of you, I dunno. Never been good in math. But suppose there were a problem that wasn't.

5. Originally Posted by question111
Book's kind of skimpy on this

Find the domain of each function.

f(x) = 5x + 4 / x^2 + 3x + 2

Thank you for any help.
Hi question111,

Like Running-gag told you, find out what makes the denominator = 0. Then the domain will be all real numbers except those values.

$x^2+3x+2=0$

$(x+2)(x+1)=0$

$x = -2 \ \ or \ \ x=-1$

So, the domain is all real numbers except -2 and -1.

6. I understand. Thank you.