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Thread: Domain for rational function

  1. #1
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    Domain for rational function

    Hi,

    My question is based on the following function:

    Domain for rational function-screen-shot-2018-01-13-11.33.58-am.png

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

    Domain for rational function-screen-shot-2018-01-13-11.34.07-am.png

    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
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    Re: Domain for rational function

    Quote Originally Posted by otownsend View Post
    Hi,

    My question is based on the following function:

    Click image for larger version. 

Name:	Screen Shot 2018-01-13 at 11.33.58 AM.png 
Views:	2 
Size:	123.7 KB 
ID:	38456

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

    Click image for larger version. 

Name:	Screen Shot 2018-01-13 at 11.34.07 AM.png 
Views:	7 
Size:	457.5 KB 
ID:	38457

    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.
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    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.
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    Re: Domain for rational function

    Quote Originally Posted by otownsend View Post
    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.
    Thanks from topsquark and otownsend
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  5. #5
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    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.
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