Re: InverseFunction[]
- To: mathgroup at smc.vnet.net
- Subject: [mg41965] Re: InverseFunction[]
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Wed, 11 Jun 2003 13:18:03 -0400 (EDT)
- Organization: NewsReader.Com Subscriber
- References: <bbt23g$nj3$1@smc.vnet.net> <bc1jh1$bjp$1@smc.vnet.net> <bc6nuj$2j3$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Paul Abbott <paul at physics.uwa.edu.au> wrote: > In article <bc1jh1$bjp$1 at smc.vnet.net>, > wself at msubillings.edu (Will Self) wrote: > > > You can easily write down a function which has an inverse, but the > > inverse cannot be expressed in closed form, or in symbols that anyone > > has invented. For example, f[x_]= x*E^x. This function is increasing > > on (for example) the interval [1,3], therefore an inverse exists, at > > least for 1 <= x <= 3. But (as far as I know) this inverse function > > has no name. > > Your point is valid. However, try Solve[x*E^x == y, x] and you'll see > Mathematica knows about the inverse function for your example. Right. It might be noted that Mathematica's name for that inverse, "ProductLog", is less common that the name "Lambert W function". By the way, seeing that InverseFunction[ProductLog] gives #1*E^#1 & as output, is there some way to use InverseFunction to get ProductLog as output? David