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Math Help - f(x) = x^1/3

  1. #1
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    f(x) = x^1/3

    ok so for this project I have to identify all this stuff for the function
    f(x) = x^{1/3}

    and a few things that I have to identify I don't know.

    1) What are intervals of continuity?
    2) Explain one-to-one

    I have no idea what both those things are. Please explain for me so that I can understand.

    Thanks!
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  2. #2
    Master Of Puppets
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    Quote Originally Posted by yoman360 View Post

    1) What are intervals of continuity?

    I think you are being asked to provide what interval fr x these function is continuous. As x can be any real number in this case then the interval for continuity would be (-\infty ,\infty)


    Quote Originally Posted by yoman360 View Post

    2) Explain one-to-one
    The term one to one means that there is only one x value for any y value (and vice versa) for the function in question.
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  3. #3
    Senior Member pacman's Avatar
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    yoman360, perhaps this graph may help you . . . .
    Attached Thumbnails Attached Thumbnails f(x) = x^1/3-yx.gif  
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  4. #4
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    Quote Originally Posted by pacman View Post
    yoman360, perhaps this graph may help you . . . .
    nice graph ... what function is it?
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  5. #5
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    Quote Originally Posted by pacman View Post
    yoman360, perhaps this graph may help you . . . .
    The range set is not specified, so wouldn't you assume Reals? In that case, an odd root can take a negative radicand and still produce a value in the Reals.
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  6. #6
    Senior Member pacman's Avatar
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    here is the much better view, domain of x is -2 to +2
    Attached Thumbnails Attached Thumbnails f(x) = x^1/3-kk.gif  
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