# Thread: Domain of a function

1. ## Domain of a function

I am trying to figure out how to write the domain in interval notation
i reduced the denominator to (x-4)^2 but am stuck now
any help would be great

Thanks

2. ## Re: Domain of a function

What you have said is not entirely correct, you can reduce the denominator to $(x+4)^2$ thus
$f(x) = \frac{x-2}{x^2+8x+16} = \frac{x-2}{(x+4)^2}$

For which value is the fraction not defined? i.e when is the denominator zero?
Can you make a conclusion now?

3. ## Re: Domain of a function

I believe the denominator is = to zero when x = to -4 or 4
so in interval notation I got (infinity,-4) U (4, inifinity)

4. ## Re: Domain of a function

Originally Posted by M670
I believe the denominator is = to zero when x = to -4 or 4
so in interval notation I got (infinity,-4) U (4, inifinity)
$f(4) = \frac{4-2}{(4+4)^2} = \frac{2}{64} = \frac{1}{32}$
thus $x=4$ is not a problem. Only $x=-4$ is a problem because then the denominator will be equal to 0.

Thus the domain is ... ?

5. ## Re: Domain of a function

correction ...

$(-\infty,-4) \cup (-4, \infty)$

only x = -4 is not in the domain.

6. ## Re: Domain of a function

The domain is all real number excluding -4

7. ## Re: Domain of a function

Originally Posted by M670
The domain is all real number excluding -4
Exactly! $\mathbb{R} \setminus \{-4\}$

8. ## Re: Domain of a function

Thank You to both of you
I have been stuck on this for over a day now