18. Let $f$ be a function on the positive real numbers such that $f ( x y ) = f ( x ) + f ( y )$. If $f ( 2024 ) = 2$ then which of the following statement(s) is/ are true? (a) $f \left( \frac { 1 } { 2024 } \right) = 1$ (b) $f \left( \frac { 1 } { 2024 } \right) = - 1$ (c) $f \left( \frac { 1 } { 2024 } \right) = - 2$ (d) $f \left( \frac { 1 } { 2024 } \right) = 2$
The following description is for questions 19 and 20.
A perfect shuffle of a deck of cards divides the deck into two equal parts and then interleaves the cards from each half, starting with the first card of the first half. For instance, if we shuffle a deck of cards containing 10 cards arranged $[ 1,2,3,4,5,6,7,8,9,10 ]$ we first create two equal decks with cards $[ 1,2,3,4,5 ]$ and $[ 6,7,8,9,10 ]$ and then interleave them to get a new deck $[ 1,6,2,7,3,8,4,9,5,10 ]$.
18. Let $f$ be a function on the positive real numbers such that $f ( x y ) = f ( x ) + f ( y )$. If $f ( 2024 ) = 2$ then which of the following statement(s) is/ are true?\\
(a) $f \left( \frac { 1 } { 2024 } \right) = 1$\\
(b) $f \left( \frac { 1 } { 2024 } \right) = - 1$\\
(c) $f \left( \frac { 1 } { 2024 } \right) = - 2$\\
(d) $f \left( \frac { 1 } { 2024 } \right) = 2$
\section*{The following description is for questions 19 and 20.}
A perfect shuffle of a deck of cards divides the deck into two equal parts and then interleaves the cards from each half, starting with the first card of the first half.
For instance, if we shuffle a deck of cards containing 10 cards arranged $[ 1,2,3,4,5,6,7,8,9,10 ]$ we first create two equal decks with cards $[ 1,2,3,4,5 ]$ and $[ 6,7,8,9,10 ]$ and then interleave them to get a new deck $[ 1,6,2,7,3,8,4,9,5,10 ]$.\\