Domains

[Rudy]

I have 2 questions.....
what is the domain for f(x) = log of the absolute value of x? I get all positive real numbers...is this right?

Also...what is the doman of 1 divided by e to the x power minus one. I don't know how to use the equation editor on this yet. My domain is all real numbers but 1...is this right?
Thanks for your help.

 

[Aladdin]

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Welcome Rudy -

\(\displaystyle 1- \ Find \ the \ domain \ of \::\ log|x|\)

\(\displaystyle Domain \ is \ R* ,for \ all \ x \ except \ zero ..\ = ]-inf,00,+inf[\)

\(\displaystyle 2- log(e^x)\)

\(\displaystyle Domain \ is \ R \ ]-inf,+inf[\)

Many Smiles

 

[Rudy]

Hi Alladin....on the second question 1 divided by the quantity of e to the x minus 1.......it can't be zero because e to the 0 would make it 1(and the denominator would be zero. Right?

 

[Aladdin]

Hi Alladin....on the second question 1 divided by the quantity of e to the x minus 1.......it can't be zero because e to the 0 would make it 1(and the denominator would be zero. Right?

Is my expression for the second correct ! I guessed that's why . . .

You meant . . . . \(\displaystyle log{\frac{1}{e^{-x}-1}\)

. . . . \(\displaystyle log{\frac{e^{x}}{1-e^{x}}\)

. . . . \(\displaystyle Domain \ is \ for \ : : \ 1-e^x >0\)

With your calculations you get : x<0 !

Kapish?! :wink: