Thread: Undefined functions

1. Undefined functions

A fraction is undefined if the denominator = 0; obviuosly...

Are there values that when you take the natural log, the result is undefined?

Are there values, say x, such that e^x is undefined?

What are they? Thanks.

2. Originally Posted by jzellt
A fraction is undefined if the denominator = 0; obviuosly...

Are there values that when you take the natural log, the result is undefined?

Are there values, say x, such that e^x is undefined?

What are they? Thanks.
ln(x) and e^x are inverse functions... so the range of the one is the domain of the other.

Where are you stuck? I think you'll learn more by trying to explain your thoughts than if I just tell you the answers..

3. I just want to make sure I can recognize anytime a function is undefined. I have an exam tomorrow and if I can't recognize this, I won't be able to work out the problems properly...

4. Originally Posted by jzellt
I just want to make sure I can recognize anytime a function is undefined. I have an exam tomorrow and if I can't recognize this, I won't be able to work out the problems properly...
I'm afraid that's not a very good excuse. Let's try graphical explanation instead.

$\displaystyle \,e^x$

http://upload.wikimedia.org/wikipedi...px-Exp.svg.png

$\displaystyle \,\log_2(x)$

http://upload.wikimedia.org/wikipedi...rithm_plot.png

See it?

5. What you want to know is the domains of those functions- and you should learn that when you learn the functions.

The domain of ln(x) is "all positive real numbers" and so ln(x) is (literally) undefined for 0 or any negative numbers.

The domain of $\displaystyle e^x$ is "all real numbers" so $\displaystyle e^x$ is defined for all real numbers.