Re: InverseFunction[]
- To: mathgroup at smc.vnet.net
- Subject: [mg41900] Re: InverseFunction[]
- From: wself at msubillings.edu (Will Self)
- Date: Mon, 9 Jun 2003 05:20:48 -0400 (EDT)
- References: <bbt23g$nj3$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Ronny Mandal" <ronnyma at math.uio.no> wrote in message news:<bbt23g$nj3$1 at smc.vnet.net>...
> Hi!
>
> Is it true that this only displays the inverse function of built-in
> mathematica-function?
>
> How do I then find the inverse of arbitrary functions?
>
> Regards, RM
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.
If you are working numerically, there is a simple trick you can use to
get an approximate inverse for a function. For the example f[x]
above, on the interval [1,3], you can do the following:
t = Table[{f[x], x}, {x, 0, 3, .1}]
g = Interpolation[t]
Plot[g[x], {x, 0, 60}]
Checking accuracy:
Table[g[f[x]], {x, 1, 3, .25}]