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

[roam]

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,

 

[Dale]

InverseFunction only evaluates for built-in functions like trig functions. I think you want:
Solve[y == (2 x + 1)/(x - 1), x]

 

[roam]

Oh I see... Thank you!

 

[iremcangun]

Thank you very much roam, you've helped me to solve a big problem.

 

[blue_raver22]

I can understand your frustration with not being able to find the inverse of a function using Mathematica. First, it's important to note that not all functions have an inverse that can be easily expressed in terms of elementary functions. In the case of the function you provided, f(x)=(2x+1)/(x-1), Mathematica is correctly giving you the inverse as InverseFunction[(1+2x)/(-1+x)]. This is a valid representation of the inverse function, but it may not be the most intuitive form for you.

One possible reason for Mathematica not producing any answers could be that the function you provided is not one-to-one, meaning that there are multiple inputs that can give the same output. In this case, the inverse function would not exist or may not be well-defined. It's always important to check the domain and range of a function when trying to find its inverse.

In general, finding the inverse of a function can be a challenging task and may require more advanced mathematical techniques. If you are looking for a more simplified or explicit form of the inverse function, you may need to use additional commands or functions in Mathematica. I would suggest consulting Mathematica's documentation or seeking assistance from a mathematician or computer scientist who is familiar with the software.

Overall, Mathematica is a powerful tool for mathematical computations, but it's important to understand the limitations and nuances of the software when using it for complex tasks such as finding inverse functions. Keep exploring and don't hesitate to seek help when needed.