Results 1 to 6 of 6

Math Help - Domain of the function y=x^(1/3)

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    29

    Domain of the function y=x^(1/3)

    Hi, I'm having trouble on finding the domain of y=x^(1/3). Mathematica is plotting the graph for x E [0,infinity). If x is a negative number, then (-x)^(1/3) is (-1)^(1/3)*(x)^(1/3) which is -(x)^(1/3) for every x and there shouldn't be any problem to graph for this domain. So why can't I take the negative numbers as a domain of this function?
    Somebody help me understand this!
    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Yep, fair point

    \sqrt[3]{-8} = -2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by patzer View Post
    Anyone?
    Computer algebra systems treat x^{\frac{1}{3}} as a expression in the complex field. MathCad does the same a Mathematica.
    However, try the notation \sqrt[3]{x}.
    Using that notation in MathCad I get the expected graph.
    I do not know the command in Mathematica.
    Last edited by mr fantastic; May 22nd 2011 at 05:02 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2010
    Posts
    29
    So, we can say that the domain of y=(x)^(1/3) is definitely for x E (-infinity, infinity), right?

    Thank you again.
    Last edited by mr fantastic; May 22nd 2011 at 05:03 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by patzer View Post
    So, we can say that the domain of y=(x)^(1/3) is definitely for x E (-infinity, infinity), right?
    For the set real numbers.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I don't know which version of Mathematica you have, but I suspect that Mathematica is actually plotting

    x^{1/3}=e^{\ln(x^{1/3})}=e^{\frac{1}{3}\,\ln(x)}.

    I'm using the equality symbol loosely here, because the instant you introduce the logarithm, you've changed the domain and therefore the function. And that's precisely your problem.

    One solution is to "trick" Mathematica into plotting everything for you by means of the command

    Plot[Sign[x](Abs[x])^(1/3),{x,-5,5}].

    So here I erase the sign information inside the cube root, and then insert it back again with the Sign function.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Domain of Function
    Posted in the Algebra Forum
    Replies: 6
    Last Post: July 4th 2010, 02:20 PM
  2. Domain of e function
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: October 16th 2009, 11:58 AM
  3. Function domain
    Posted in the Algebra Forum
    Replies: 10
    Last Post: May 17th 2009, 03:16 PM
  4. a domain of a function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 1st 2008, 10:20 AM
  5. domain of function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 13th 2006, 03:22 AM

Search Tags


/mathhelpforum @mathhelpforum