Function inversion

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What is the criteria to know whether a function may be inverted into an elementary functional form?
 

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HallsofIvy
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Define "elementary functional form".

Any function that is "one to one" from set A onto set B then can be inverted ito an inverse function from B to A.

Do you consider "ln(x)" and "ex" "elementary functional forms"? Since a common definition of "ln(x)" is "the inverse of ex (and if it is defined in other ways, ex is defined as "the inverse of ln(x)"), I guess you would agree that any "elementary functional form" that has an inverse can be inverted into "elementary functional form".
 

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