Re: plotting even function

[John B. Thoo]

Hi, Steve.  I'm sorry for dragging this out, but I'm not yet 
understanding.

Why is

  x^(2/3) equal to (x^(1/3))^2

but

  x^(2/3) not equal to (x^2)^(1/3)?

Also, why is  (x^(1/3))^2  not even?  If  f(x) = (x^(1/3))^2,  then 
isn't

  f(-x) = ((-x)^(1/3))^2 = (- x^(1/3))^2 = (x^(1/3))^2 = f(x)

(for real  x)?  I must not be understanding something rudimentary.

TIA.

---John.
(a numerical computation and Octave novice)


On Mar 19, 2005, at 5:03 PM, Steve C. Thompson wrote:

> John,
>
> Could this be it?
>
>   x^(2/3) is equal to (x^(1/3))^2 which isn't even.
>
>   x^(2/3) is not equal to (x^2)^(1/3) which is even.
>
>
> Steve
>
>
> On Mar 19 16:20PM, John B. Thoo wrote:
> > Hi.  I hope that I'm not embarrassing myself by asking the following.
> >
> > I believe that
> >
> >        3       2/3    1
> >   y = --- (2 x)    + ---
> >        4              2
> >
> > is an even function, yet
> >
> > x = -1:0.04:1;
> > plot (x, 0.75 * (2 .* x).^(2 / 3) + 0.5)
> >
> > is not symmetrical about the y-axis.  What is wrong with my thinking?
> >
> > TIA.
> > ---John.
> >
> >
> >
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