Evaluate the Following Function For $f ( x ) = - 2 x ^ { 2 } + 1$

Multiple Choice

Evaluate the following function for $f ( x ) = - 2 x ^ { 2 } + 1$ and $g ( x ) = x + 4$ algebraically.
$$\left( \frac { f } { g } \right) ( q - 4 )$$

A) $\frac { - 2 q ^ { 2 } + 5 } { q + 8 }$
B) $\frac { - 2 q ^ { 2 } + 8 q - 31 } { q }$
C) $\frac { - 2 q ^ { 2 } + 5 } { q }$
D) $\frac { - 2 q ^ { 2 } + 16 q - 31 } { q }$
E) $\frac { - 2 q ^ { 2 } - 3 } { q }$