Finding the Inverse of a 5th-Order Polynomial Function Find the inverse of: $F(x)=7x^5-5x^3-3x^2+2x$.
 A: What you are given is a function $F(x)$, not an equation.
Start with $F(x) = y = 7x^5 - 5x^3 - 3x^2 + 2x$.
Exchange $x$ and $y$:
$x = 7y^5 - 5y^3 - 3y^2 + 2y= y(7y^4 - 5 y^2 - 3y + 2)$ and "solve" for $y$ to express it in terms of $x$, but rename $y$ as $y^*$ to avoid confusion with the rest of the description of the most frequent technique for finding the inverse of a function, in general.
(In this case, this will not be terribly easy, algebraically!)
Then $F^{-1}(x) = y^*$

I just saw your comment: is this the approach you tried?
A: 
$f(x),x,f^{-1}(x)$ in same plot. Maybe this can help  if you want to see behavior of curves or find number of intersections.
A: If you use Mathematica, here's what I'd do:
Make a table of small increments
mytable = Table[{ f [x] , x } , {x, 0, 10, 0.01} ]
Then you can plot this and get a visual representation of the inverse.
If you want the analytical inverse, just use the Fit function on this table to get a polynomial like this:
myfit = Fit[mytable, {1, x, x^2, x^3, x^4}, x]
This will at least get you a polynomial function that is the inverse, though it won't be the true inverse, just an approximation.
