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: <email@example.com>
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