A cubic function $f ( x )$ with leading coefficient 1 and a function $g ( x )$ that is continuous on the set of all real numbers satisfy the following conditions. Find the value of $f ( 4 )$. [4 points]\\
(가) For all real numbers $x$,
$$f ( x ) = f ( 1 ) + ( x - 1 ) f ^ { \prime } ( g ( x ) )$$
(나) The minimum value of the function $g ( x )$ is $\frac { 5 } { 2 }$.\\
(다) $f ( 0 ) = - 3$, $f ( g ( 1 ) ) = 6$