Hi, I'm new here and new to Mathematica also.
So, I was defining two functions, s1 and s2. Both are the same functions but one was simplified after the integration and the other one wasn't.
So I calculate the inverse of these functions (and once they are the integral of the same function, I expect that the inverses would return the same values) and that is not happening.
I would like to understand why the Simplify cause the inverse equations to have different solutions.
I'm adding a notebook to demonstrate my question:
If anyone can help, I really would appreciate it
Thank you very much in advance
The culprit is PowerExpand, not Simplify. The two forms s1 and s2 are not totally equivalent. Also, you should expect trouble when inverting a function that is not invertible over the complexes:
Solve[s1[a, b, tt] == x, tt]
You will see that there are two branches. It seems that InverseFunction chooses the first one, which involves the logarithm of a negative number (if a>0). With s2 the formulas are different:
Solve[s2[a, b, tt] == x, tt]
and InverseFunction makes its choice.
The output of InverseFunction should be carefully sanity-checked each time.
Thank you for your quick and precise response!
I really will be more careful about the use of the InverseFunction and certainly need to study more about complex numbers and functions.
Once again, thank you very much.
BTW: your website is great. I'm discovering a lot of interesting content there. And I only can imagine the experience you have acumulated using this amazing software for so long (since 1991, right?).
Wow, thank you, I hadn't noticed that I have been using Mathematica for 30 years now!