# Simplify[ ] affects InverseFunction[ ]?

Posted 9 days ago
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 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 .
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Posted 8 days ago
 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.