The function $f$ is defined on the positive integers as follows: $$f ( 1 ) = 5 , \text { and for } n \geqslant 1 : \quad \begin{array} { l l }
f ( n + 1 ) = 3 f ( n ) + 1 & \text { if } f ( n ) \text { is odd } \\
& f ( n + 1 ) = \frac { 1 } { 2 } f ( n )
\end{array} \text { if } f ( n ) \text { is even }$$ The function $g$ is defined on the positive integers as follows: $$\begin{array} { l l }
g ( 1 ) = 3 , \text { and for } n \geqslant 1 : \quad & g ( n + 1 ) = g ( n ) + 5 \\
& \text { if } g ( n ) \text { is odd } \\
g ( n + 1 ) = \frac { 1 } { 2 } g ( n ) & \text { if } g ( n ) \text { is even }
\end{array}$$ What is the value of $f ( 1000 ) - g ( 1000 )$ ? A - 6 B - 5 C 1 D 2 E 4 F 8
& B
The function $f$ is defined on the positive integers as follows:
$$f ( 1 ) = 5 , \text { and for } n \geqslant 1 : \quad \begin{array} { l l }
f ( n + 1 ) = 3 f ( n ) + 1 & \text { if } f ( n ) \text { is odd } \\
& f ( n + 1 ) = \frac { 1 } { 2 } f ( n )
\end{array} \text { if } f ( n ) \text { is even }$$
The function $g$ is defined on the positive integers as follows:
$$\begin{array} { l l }
g ( 1 ) = 3 , \text { and for } n \geqslant 1 : \quad & g ( n + 1 ) = g ( n ) + 5 \\
& \text { if } g ( n ) \text { is odd } \\
g ( n + 1 ) = \frac { 1 } { 2 } g ( n ) & \text { if } g ( n ) \text { is even }
\end{array}$$
What is the value of $f ( 1000 ) - g ( 1000 )$ ?
A - 6
B - 5
C 1
D 2
E 4
F 8