Why Doesn't Mathematica Produce an Explicit Inverse for My Function?

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Discussion Overview

The discussion revolves around the challenges of finding the inverse of a specific function, f(x)=(2x+1)/(x-1), using Mathematica. Participants explore the limitations of the InverseFunction command and suggest alternative methods for obtaining the inverse.

Discussion Character

  • Technical explanation, Homework-related

Main Points Raised

  • One participant notes that Mathematica's InverseFunction does not produce explicit inverses for user-defined functions, only for built-in functions.
  • Another participant suggests using the Solve function to find the inverse by setting up the equation y == (2 x + 1)/(x - 1) and solving for x.
  • A later reply expresses gratitude for the clarification and assistance provided.

Areas of Agreement / Disagreement

Participants appear to agree on the limitation of the InverseFunction command and the proposed alternative method using Solve, indicating a shared understanding of the issue.

Contextual Notes

There may be assumptions regarding the familiarity with Mathematica and its functions, as well as the definitions of inverse functions that are not explicitly stated.

roam
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I'm trying to find the inverse of a function, for instance: f(x)=(2x+1)/(x-1) using Mathematica but it doesn't produce any answers.

This is my input:

> f(x)=(2x+1)/(x-1)

> InverseFunction[f]

The output is always something like:

"InverseFunction[(1+2x)/(-1+x)]"

So, does anyone know what the problem is?

Thanks,
 
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InverseFunction only evaluates for built-in functions like trig functions. I think you want:
Solve[y == (2 x + 1)/(x - 1), x]
 
Oh I see... Thank you! :smile:
 
Thank you very much roam, you've helped me to solve a big problem.
 

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