Try to plot x^(2/3).. what happen for x<0 ?
08-22-2019, 03:45 AM (This post was last modified: 08-22-2019 03:46 AM by josephec.)
Post: #1
 josephec Junior Member Posts: 31 Joined: Jan 2014
Try to plot x^(2/3).. what happen for x<0 ?
Hi Friends

Why In HP PRIME is different
(X^2)^(1/3) and (x^(1/3))^2 ?

Pd. The first one plots for x<0

08-22-2019, 06:45 AM
Post: #2
 rkf Member Posts: 69 Joined: Apr 2014
RE: Try to plot x^(2/3).. what happen for x<0 ?
I assume the Prime does simpy follow the basic rules of Mathematics:

In the first expression, we start with squaring x, which yields for all reals a positive result - thus the cubic root is defined everywhere.

In the second expression, the cubic root is calculated first - but for reals is only defined for x >= 0. Thus the plot is left for x < 0.
08-22-2019, 08:08 AM (This post was last modified: 08-22-2019 08:10 AM by ijabbott.)
Post: #3
 ijabbott Senior Member Posts: 1,211 Joined: Jul 2015
RE: Try to plot x^(2/3).. what happen for x<0 ?
You can redefine the second one as $$\big( \sqrt[3]{x}\big)^2$$ to square the real cube root of $$x$$.

Note that $$x^\frac{1}{3}$$ and $$\sqrt[3]{x}$$ are treated differently, and that $$x^\frac{1}{3}$$ usually produces a complex number when $$x < 0$$, and its square is also complex, so it cannot be plotted by the Function app.

— Ian Abbott
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