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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
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