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Re: How to obtain numberical value from an InverseFunction?

• To: mathgroup at smc.vnet.net
• Subject: [mg80945] Re: How to obtain numberical value from an InverseFunction?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 6 Sep 2007 05:23:21 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <fblkie$sac$1@smc.vnet.net>

Nasser Abbasi wrote:

> Are inverse function in Mathematica only have symbolic form and can't be 
> used to evaluate numerically?
 >
> Anything I am trying is not working, this is a very simple example:
> 
> f[x_] := x
> InverseFunction[f][x]
> 
> Now, how to evaluate anything out of the above? say for x=0.5, I expected to 
> get .5, but all I get is just
> f(^-1)[x][.5]
> 
> any ideas? Very little help on InverseFunctions.

If Mathematica knows explicitly the inverse function of a given function 
(say ArcSin for Sin), then it uses it. Otherwise, InverseFunction is 
used symbolically. To get a numeric answer, you could use FindRoot for 
instance. See

"Inverse Functions"
http://reference.wolfram.com/mathematica/guide/InverseFunctions.html

(Note that InverseFunction is titled "symbolic functional inverse.")

The parts of the following sections of _The Mathematica Book_ are of 
particular interest regarding this question.

"2.2.9 Advanced Topic: Working with Operators"
http://documents.wolfram.com/mathematica/book/section-2.2.9

"3.4.2 Equations in One Variable"
http://documents.wolfram.com/mathematica/book/section-3.4.2

"2.2.1 Function Names as Expressions"
http://documents.wolfram.com/mathematica/book/section-2.2.1

"1.5.7 Solving Equations"
http://documents.wolfram.com/mathematica/book/section-1.5.7

Also, sections 3.8 and 6.5.1 of Michael Trott's _The Mathematica 
GuideBook for Programming_, are worth reading too.

Regards,
-- 
Jean-Marc