Finding the Inverse Function Value

Consider the function defined by the equation:

$$ f(x) = 2x^3 - 6x^2 + 4 $$

To investigate the characteristics of the function, we want to find the value of the inverse function, denoted as $$ f^{-1}(y) $$, for the input value $$ y = 6 $$. In other words, determine the value(s) of $$ x $$ such that $$ f(x) = 6 $$.

Once you have those values, calculate the geometric mean of all the solutions and enter your answer in the grid below.