Re: Inverse Function
- To: mathgroup at smc.vnet.net
- Subject: [mg123631] Re: Inverse Function
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Tue, 13 Dec 2011 05:44:32 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201112121143.GAA12844@smc.vnet.net>
- Reply-to: murray at math.umass.edu
Welcome to Mathematica!
1. You seem to have 5 variables involved in your expression: y, ax, b,
cx, and d. That's not what you really meant, is it?
Presumably you meant a x and c x instead of ax and cx. (Remember,
symbols can have multi-character names. So you need either a space or an
explicit multiplication sign * between "a" and "x", and between "c" and
"x". Unless, that is, you didn't really intend a and c to be symbolic
but were specific numeric constants -- e.g., 3x and 5x.)
2. You did not give us a function. Rather, you gave us an equation,
y=(ax +b)/(cx+d).
Presumably you want the function that one would define in
Mathematica by:
y[x_]:= (a x + b)/(c x + d)
3. Did you try looking up "inverse function" in Mathematica's
Documentation Center?
The search returns, among others, items "Inverse", "Inverse
Functions", and "InverseFunction". The last of these looks most
relevant. Following examples there, try:
InverseFunction[y]
The result you'll get (shown here in InputForm) is:
(-b + d*#1)/(a - c*#1) &
That's a "pure function" -- a function that's anonymous, where the
"Slot" variable #1 stands for the input variable.
If you wish, you can give that function a name:
yInv = InverseFunction[y]
And then use it just like any other function, e.g.:
yInv[3I]
(-b + (3*I)*d)/(a - (3*I)*c)
Again, I showed the result in one-dimensional InputForm rather than the
usual two-dimensional StandardForm.
Hope this helps.
On 12/12/11 6:43 AM, Harry Har wrote:
> Hi, All,
>
> I'm newbie in Mathematica. I want to find the inverse function of y=(ax
> +b)/(cx+d). How to to this in Mathematica? Many thank's.
>
> Harry.
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
- References:
- Inverse Function
- From: Harry Har <harryhar800@gmail.com>
- Inverse Function