[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: plotting even function
From: |
Gunnar |
Subject: |
Re: plotting even function |
Date: |
Tue, 22 Mar 2005 13:38:54 +0100 |
User-agent: |
KMail/1.7.2 |
On Sunday 20 March 2005 18.09, Geraint Paul Bevan wrote:
> John B. Thoo wrote:
> > 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)
>
> It is not true to say that (-x)^(1/3) is the same as -(x^(1/3)). That
> is one possibility but there are two more. If n is an integer, x^n has
> a unique value but x^(1/n) has n possible values i.e. the square root
> x^(1/2) has two possible values, the cube root x^(1/3) has three
> possible values, etc.
Isn't that just a matter of definition and our frames of references?
What do we mean when we talk about a^(1/3) ? In simple real analysis it means
the positive solution, x, to the equation x^3=a for a>0, and when a<0 it is
then -x where x is the positive solution to x^3= -a. At this level x^(2/3)
is even.
It's not even when you have studied complex analysis, but of course, then you
know how to make it an even function, and you can also make it a not-even,
and not-odd function.
I must say that I enjoyed reading this discussion.
B.t.w. Maple does not plot anything for negative x-values for the function
x^(2/3). It also does not simplify (-1)^(2/3) to -1.
Cheers,
Gunnar.
-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.
Octave's home on the web: http://www.octave.org
How to fund new projects: http://www.octave.org/funding.html
Subscription information: http://www.octave.org/archive.html
-------------------------------------------------------------
- Re: plotting even function, (continued)
- Re: plotting even function, Henry F. Mollet, 2005/03/19
- Re: plotting even function, Geraint Paul Bevan, 2005/03/19
- Re: plotting even function, Thomas Shores, 2005/03/19
- Re: plotting even function, Thomas Shores, 2005/03/19
- Re: plotting even function, John B. Thoo, 2005/03/20
- Re: plotting even function, mavram, 2005/03/20
- Re: plotting even function, Geraint Paul Bevan, 2005/03/20
- Re: plotting even function, Mike Miller, 2005/03/20
Re: plotting even function, Thomas Shores, 2005/03/19
Re: plotting even function,
Gunnar <=