Plotting (x^3 - x^2)^(1/3) gives unexpected results

Question

I have a function

 g[x_] := (x^3 - x^2)^(1/3)

that I want to plot. The plot I am getting gives me strange results. There is nothing plotted for x < 1, contrary to the results that I can obtain from my calculator. Do you have a idea why?

You need to cut and paste both the code for the function and the code you used to Plot that failed to work properly. It might be related to the result creating an imaginary number. — Jack LaVigne, Oct 07 '15 at 19:15
The function is imaginary for certain values of x. You can see the real part of the solution by plotting Plot[Re@g[x],{x,0,2}] Also, I second Jack LaVinge. — N.J.Evans, Oct 07 '15 at 19:17
Yes but i use mathematica exchange with my phone because i have issues with my connection at the moment. Thank you for your understanding. — Bendesarts, Oct 07 '15 at 19:17
But as it is a ^(1/3) cubic roots normally the function is defined on R,isn t it? — Bendesarts, Oct 07 '15 at 19:27

score 5 · Accepted Answer · answered Oct 07 '15 at 19:30

5

You probably want to use Surd rather than Power. Mathematica normally treats expressions as complex-valued, which may give results differing from most calculators, which are restricted to the reals. Surd is provided to give calculator-like behavior when that is desired.

g[x_] := Surd[x^3 - x^2, 3]
With[{a = 3}, Plot[g[x], {x, -a, a}]]

answered Oct 07 '15 at 19:30

m_goldberg

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Perfect thank you and do you know what is the origin of this label "Surd"? – Bendesarts Oct 07 '15 at 19:38
2

@Bendesarts. I believe it is an old word pertaining to the extraction of irrational roots of integers; recall that "absurd" and "irrational" are practically synonyms. – m_goldberg Oct 07 '15 at 19:43
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Or use CubeRoot. – Daniel Lichtblau Oct 07 '15 at 19:49

Plotting (x^3 - x^2)^(1/3) gives unexpected results

1 Answers1