2
$\begingroup$

Yesterday our analysis professor told us you cannot solve $$ y = e^x+2/(1+x^2) $$ for x, but you have the option to approximate this numerically. He did not prove that, he just noted it.

I can't believe that's true and am very unsatisfied with that. How do I solve this for x? If I don't, why is that?

  • 0
    I'd like to see how an inverse function is constructed.2012-11-29
  • 3
    *Proving* that an equation cannot be solved using *elementary functions* is very difficult, and seldom done. There is moderately good theory (differential algebra) that deals with integration in elementary terms, and this can sometimes be adapted to inverse functions. From experience, one can *guess* that there is no *elementary function* $g$ such that $g(y)=x$. I doubt that this has ever been proved.2012-11-29

1 Answers 1