How to find an inverse of this function

Question

So I am aware of the general rules to follow to find an inverse of a function, but it seems like I'd need something different for this one:

$$f(x) = -2x^3-7x+5$$

if I try what I'm use it I end up with something like :

$$x-5 = -2y^3-7y$$

and I'm not sure how to proceed. Is there a way to find this using derivatives?

Answer 1

According to Wolfy, the real solution to "solve $2 x^3+7 x-5 = y$ for x" is, after a bunch of formatting,

$x = \dfrac{\sqrt[3]{\sqrt{3} \sqrt{27 y^2+270 y+1361}+9 y+45}}{6^{2/3}} -\dfrac{7}{6^{1/3} \sqrt[3]{\sqrt{3} \sqrt{27 y^2+270 y+1361}+9 y+45)}} $.

There are two conjugate complex roots with expressions of similar complexity.