12. Let the function $f ( x )$ and its derivative $f ^ { \prime } ( x )$ both have domain $\mathbf { R }$. Let $g ( x ) = f ^ { \prime } ( x )$. If $f \left( \frac { 3 } { 2 } - 2 x \right)$ and $g ( 2 + x )$ are both even functions, then\\
A. $f ( 0 ) = 0$\\
B. $g \left( - \frac { 1 } { 2 } \right) = 0$\\
C. $f ( - 1 ) = f ( 4 )$\\
D. $g ( - 1 ) = g ( 2 )$
\section*{III. Fill-in-the-Blank Questions: This section contains 4 questions, each worth 5 points, for a total of 20 points.}