For a programming project, I'm trying to figure out the inverse of a quadratic function: $f(x) = ax^4 + bx^3 + cx^2 + dx + e$. In my case, the numbers $a$, $b$, $c$, $d$ and $e$ are all known constants, but rather annoying non-integers going about five places past the decimal point.
I have a function that returns the result when $x$ is processed through the equation, but what I now need is a function that will return the result back to the original input.
Is there an inverse to the function above, which I would be able to re-use the same constants? If I have to go about finding this solution myself, are there any resources that will explain the steps involved in simple language?
It's been twenty years since my last math class, and I don't recall ever getting into solving fourth degree equations. I've found all sorts of information about trying to solve and find the roots for quartic equations, although I don't quite understand what they're doing, but nothing on a plain old inverse of the function.