Let $f ( x )$ be a cubic function with positive leading coefficient, and for a real number $t$, let the function $$g ( x ) = \left\{ \begin{array} { r r }
- f ( x ) & ( x < t ) \\
f ( x ) & ( x \geq t )
\end{array} \right.$$ be continuous on the set of all real numbers and satisfy the following conditions. (가) For all real numbers $a$, the value of $\lim _ { x \rightarrow a + } \frac { g ( x ) } { x ( x - 2 ) }$ exists. (나) The set of natural numbers $m$ such that $\lim _ { x \rightarrow m + } \frac { g ( x ) } { x ( x - 2 ) }$ is negative is $\left\{ g ( - 1 ) , - \frac { 7 } { 2 } g ( 1 ) \right\}$. Find the value of $g ( - 5 )$. (Given that $g ( - 1 ) \neq - \frac { 7 } { 2 } g ( 1 )$) [4 points]
Let $f ( x )$ be a cubic function with positive leading coefficient, and for a real number $t$, let the function
$$g ( x ) = \left\{ \begin{array} { r r }
- f ( x ) & ( x < t ) \\
f ( x ) & ( x \geq t )
\end{array} \right.$$
be continuous on the set of all real numbers and satisfy the following conditions.\\
(가) For all real numbers $a$, the value of $\lim _ { x \rightarrow a + } \frac { g ( x ) } { x ( x - 2 ) }$ exists.\\
(나) The set of natural numbers $m$ such that $\lim _ { x \rightarrow m + } \frac { g ( x ) } { x ( x - 2 ) }$ is negative is $\left\{ g ( - 1 ) , - \frac { 7 } { 2 } g ( 1 ) \right\}$.\\
Find the value of $g ( - 5 )$. (Given that $g ( - 1 ) \neq - \frac { 7 } { 2 } g ( 1 )$) [4 points]