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## Main Question or Discussion Point

p=ax^3+bX^2+cX is positive monotonic and has an inverse X=G(p)

But I can't invert it. Is there an analytic solution?

For given parameter values I can plot numeric values- it has a tilted S shape.

But I can't invert it. Is there an analytic solution?

For given parameter values I can plot numeric values- it has a tilted S shape.