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Functions with parameters?

• To: mathgroup at smc.vnet.net
• Subject: [mg22214] Functions with parameters?
• From: tautenhahn at fichtelgebirge.org (Nikolas Tautenhahn)
• Date: Fri, 18 Feb 2000 02:34:51 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi there!

I have Mathematica 4 and I want to discuss a simple function with a
parameter; The problem, however, is that I neither found some help in
the online help of Mathematica nor in the book (which is about
Mathematica 3) by Michael Kofler.
I don't know if it is possible to do everything I want to do with
Mathematica and that's why I'm asking here.
The function I want to discuss is

f(x)=ln(x/(x-a) with a>0
ok, in Mathematica you type f[x_]=Log[x/(x-a)].
what I want to do is:

* where is this function defined (I don't know if this is the right
English word; for example 1/x is *not* defined for x=0; i hope you
understand what I mean);

* derivatives etc. --> no problem, but again: where is f'(x) defined?

* Plot the function for several values of a


Thanks in advance from a newbie
Nikolas Tautenhahn