There is a quartic function $f ( x )$ with leading coefficient 1, $f ( 0 ) = 3$, and $f ^ { \prime } ( 3 ) < 0$. For a real number $t$, define the set $S$ as
$$S = \{ a \mid \text{the function } | f ( x ) - t | \text{ is not differentiable at } x = a \}$$
and let $g ( t )$ be the number of elements in set $S$. When the function $g ( t )$ is discontinuous only at $t = 3$ and $t = 19$, find the value of $f ( - 2 )$. [4 points]