       Re: Inverse of a six-parameter asymmetric sigmoidal curve

• To: mathgroup at smc.vnet.net
• Subject: [mg111221] Re: Inverse of a six-parameter asymmetric sigmoidal curve
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sat, 24 Jul 2010 05:06:06 -0400 (EDT)

```On 7/23/10 at 7:08 AM, aspiess at uke.de (spiceman) wrote:

>does anybody have a clue how to get Mathematica to deliver the
>inverse of the following function?

>fct := c + (k * Log[x]) + (d - c)/(1 + Exp[b*(Log[x] - Log[e])])^f
>Solve[fct == y, x]

>Solve::tdep: The equations appear to involve the variables to be
>solved for in an essentially non-algebraic way.

>I suppose I have to transform somehow. Any clues? Omitting k*Log[x]
>works...

Your expression has the form k*Log[x]+ p[x] where p is a
polynomial. Deleting the k*Log[x] makes your expression a
polynomial which Solve can deal with. Leaving the k*Log[x] in
makes it so that there is no closed form general solution. The
only way to solve this is to insert specific numeric values for
the coefficients and use one of the various numeric routines in
Mathematica such as FindRoot to get a numeric solution for x.

```

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