Domain

Oct 2019
42
1
united states
Find the domain of f. Write your answer using interval notation.

8x/x2 + 9, I tried moving the 9 given me x2=-9 so x= square room of -9 that is impossible, I am pretty confused.
 

Plato

MHF Helper
Aug 2006
22,490
8,653
Find the domain of f. Write your answer using interval notation.
8x/x2 + 9, I tried moving the 9 given me x2=-9 so x= square room of -9 that is impossible, I am pretty confused.
Well until you learn to post your questions in a correct format you will remain confused!
Here is exactly what you posted: \(\displaystyle \frac{8x}{x^2}+9\) is that what you meant? I think not.
I think that you meant: \(\displaystyle \frac{8x}{x^2+9}\) which has domain, all real numbers.
 
Oct 2019
42
1
united states
Yes sorry for the confusion. I am not good with technology thanks for your help.
 

Debsta

MHF Helper
Oct 2009
1,343
620
Brisbane
A rational expression, like the one you have, is undefined when the denominator is 0.
I think you may have then tried to solve \(\displaystyle x^2 +9 =0\) getting \(\displaystyle x^2=-9\). As you said, this is impossible. So far, so good.

Now, the domain of a function is the set of all numbers that x can be. Now, is there any value of x that makes this rational expression undefined? No there isn't because, as you said, there is no x-value that when squared gives -9.

So therefore x can be anything, so the domain is the set of all real numbers (there's nothing that x can't be!)