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What is the domain of this function $f(x)=3x^{\frac{2}{3}}-x$ ?

I thought it should be $\mathbb{R}$. For example, if $x=-1$, then $f(-1)=3\cdot(-1)^{\frac{2}{3}}-(-1)=3\cdot 1+1=4$. However, when I try to draw/plot this function. Many softwares, such as Mathematica and Matlab show that there are no points for $x<0$.

So I do not know why. Could anyone give me an explanation? Thanks.

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Zongxiang Yi
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    Related: https://math.stackexchange.com/questions/317528/how-do-you-compute-negative-numbers-to-fractional-powers Read thoroughly – Soumil Gupta Nov 22 '21 at 11:17
  • If you type this in WolframAlpha, a link shows up saying "use the real-valued root instead." Click on that. The domain is, as you said, all $x\in\mathbb{R}$. – bjorn93 Nov 22 '21 at 11:28

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This is just a matter of how those Softwares handle non-integer powers. In Mathematica, you should use CubeRoot[x] instead of x^(1/3). This way tou get the graph: enter image description here

PierreCarre
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