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Do you know how I could compute the inverse function of the following polynomial?

$f(x) = x^5+x^3+x$

Thanks in advance.

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    Wolfram|Alpha only gives numerical approximate solutions for $f(x)=2$, so there is probably no formula for the inverse of $f$, though I haven't checked that the Galois group of $f$ is not solvable.2012-12-01

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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.

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    We're not looking for the roots of $f(x)$, we're looking for the *inverse* of $f$, so roots of $f(x)-c$.2012-12-01