Confirmation needed

• Oct 2nd 2008, 03:09 PM
Desperation
Confirmation needed
So I'm just about done with my latest assignment, however there's this little vermin impeding my way towards a perfect score. I think I may have nailed the answer, but given that it's my last available attempt at submitting a response, I want to be extra sure.

Some background information before the actual question:

The function...
http://i23.photobucket.com/albums/b3...capture-10.png

The expression $f(x)$ is defined exactly on the set...
http://i23.photobucket.com/albums/b3...apture-4-1.png

The expression $f(x)$ is equal to zero if $x$ is equal to...
http://i23.photobucket.com/albums/b3...apture-1-4.png

The set of all real numbers $x$ for which $f(x)$ is defined and non-zero is...
http://i23.photobucket.com/albums/b3...apture-2-1.png

And so, here is what's currently holding me back...

By analyzing the sign of $f(x)$ on the above open intervals, solve the inequality...
http://i23.photobucket.com/albums/b3...apture-5-1.png
... expressing answer in interval notation.

http://i23.photobucket.com/albums/b3...apture-3-1.png

• Oct 2nd 2008, 03:29 PM
skeeter
yes.
• Oct 2nd 2008, 03:52 PM
Desperation
Quote:

Originally Posted by skeeter
yes.

Why thank you. The answer was submitted and it indeed was correct.

There's one little thing picking my interest though, why exactly can the function not be ± $e$^(8/3)? In other words, $x=0$?

Is there some $Ln$ rule I'm forgetting?
• Oct 2nd 2008, 04:14 PM
skeeter
Quote:

Originally Posted by Desperation
Why thank you. The answer was submitted and it indeed was correct.

There's one little thing picking my interest though, why exactly can the function not be ± $e$^(8/3)? In other words, $x=0$?

Is there some $Ln$ rule I'm forgetting?

If I interpret you correctly ...

x cannot equal 0 because $\ln(0)$ is undefined and x = 0 would also make the denominator of the function 0 ... undefined again.

the function equals 0 at $x = \pm e^{\frac{8}{3}}$ ... that's fine, but the inequality in question only asked for those values where the function was greater than 0 ... not 0.
• Oct 2nd 2008, 04:32 PM
Desperation
Quote:

Originally Posted by skeeter
If I interpret you correctly ...

x cannot equal 0 because $\ln(0)$ is undefined and x = 0 would also make the denominator of the function 0 ... undefined again.

the function equals 0 at $x = \pm e^{\frac{8}{3}}$ ... that's fine, but the inequality in question only asked for those values where the function was greater than 0 ... not 0.

I was referring to the set of all real numbers $x$ for which $f(x)$ is defined and non-zero; I was wondering why it excluded ± $e$^(8/3).