Is the statement true or false : inverse function of elementary function is also elementary
I think it would not be true, but i can’t find any counterexample(non-elementary inverse of elementary function)
Is there any counterexample of this?
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There are some like this one. Multiplying/adding a linear and nonlinear function, like $\sin(x),e^x$, also very likely makes the inverse nonelementary – Тyma Gaidash Jan 16 '24 at 23:25
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If $~f(x) = Ax^5 + Bx^4 + Cx^3 + Dx^2 + E,~$ then what is the inverse function to $~f(x)~?$ – user2661923 Jan 17 '24 at 01:14
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The only possible exception I could think of is inverse ("arc") trig ratios. Calculating sine as a function is simple, but I'm not sure how to calculate the arcsine as a function, I just "work it backwards". – John Jan 17 '24 at 10:59