Do you know how I could compute the inverse function of the following polynomial?
$f(x) = x^5+x^3+x$
Thanks in advance.
This function probably won't have a nice inverse, since finding the inverse is equivalent to solving the equation $f(x)=c$, or equivalently finding the roots of the equation $x^5+x^3+x-c=0$. This is a quintic polynomial, and as such probably will likely not have a general solution (i.e. for all $c$) in terms of radicals. The best you can do is usually some kind of numerical method.