How is called the class of functions whose inverse function is a polynomial? Is there any study of such functions?

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Zackery Harvey · Accepted Answer

The functions you&#039;re interested in are a particular subset of the algebraic functions. To be specific, an algebraic function   f  (  x  ) is a function that satisfies      a    n    (  x  )  f  (  x      )    n    +      a          n      −      1        (  x  )  f  (  x      )          n      −      1        +  ⋯  +      a    0    (  x  )  =  0where the       a    i    (  x  ) are polynomials. By contrast, let  P  (  x  )  =      b    n        x    n    +      b          n      −      1            x          n      −      1        +  ⋯  +      b    0  be an arbitrary polynomial. Its inverse,       P          −      1        (  x  ), satisfies  P  (      P          −      1        (  x  )  )  =      b    n        P          −      1        (  x      )    n    +      b          n      −      1            P          −      1        (  x      )          n      −      1        +  ⋯  +      b    0    =  x  .So inverses of polynomials are those algebraic functions for which the defining coefficient functions       a    i   are constants, except for the last, which is a constant minus   x.

How is called the class of functions whose inverse function

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