The function given is f(x) = 3x^3 + 2x - 1. The graph of this function is:

The point of intersection of f(x) = 3x^3 + 2x - 1 and y = 1 is the real solution of the equation

3x^3 + 2x - 1 = 1

=> 3x^3 + 2x - 2 = 0

This is a very complex cubic equation and it has one real root that can be determined using a cubic calculator. The result is x = `(sqrt(89)/27+1/3)^(1/3)-2/(9*(sqrt(89)/27+1/3)^(1/3))`

The point of intersection of f(x) = 3x^3 + 2x - 1 and y = 1 is `((sqrt(89)/27+1/3)^(1/3)-2/(9*(sqrt(89)/27+1/3)^(1/3)),1)`