# Thread: Domain for rational function

1. ## Domain for rational function

Hi,

My question is based on the following function:

I would like to know whether this domain for the function is correct:

I personally don't think it is right - I thought that when it came to cubed roots, that there were no two solutions to the answer. Can someone clarify this for me?

- otownsend

2. ## Re: Domain for rational function

Originally Posted by otownsend
Hi,

My question is based on the following function:

I would like to know whether this domain for the function is correct:

I personally don't think it is right - I thought that when it came to cubed roots, that there were no two solutions to the answer. Can someone clarify this for me?

- otownsend
Sorry to inform you but $\pm\sqrt[3]{-4}$ really makes no sense. The domain is $\mathbb{R}\setminus\{\sqrt[3]{-4}\}$
That is: the set of all real numbers except the cube root of negative four.

3. ## Re: Domain for rational function

Actually, there is no need to say sorry. This was something my teacher posted and thought was wrong, so I'm glad that I'm right.

4. ## Re: Domain for rational function

Originally Posted by otownsend
Actually, there is no need to say sorry. This was something my teacher posted and thought was wrong, so I'm glad that I'm right.
That's a pretty gruesome mistake for your teacher to make.

The cube function is one to one.

5. ## Re: Domain for rational function

If you cube a negative number, you get a negative. So that means the cube root of a negative number is a negative number.

In general, there is no way to take an EVEN power of a number to get a negative, so it's impossible to have an EVEN root of a negative number. But since any negative number taken to an ODD power is always negative, you CAN have an odd root of a negative number.