Is this related to some Physics concepts?

I am guessing that we need to define a function called P that will map like this P(f(x)) = f(-x).

$\displaystyle P\sin{x} = -\sin{x} \Rightarrow P(x) = -x$

$\displaystyle Pe^{-x} = $$\displaystyle e^{x}\Rightarrow P(x) = \frac1{x} $

$\displaystyle P(e^{x} + e^{-x}) = $$\displaystyle e^{-x} + e^{x} \Rightarrow P(x) = x$

Hopefully Topsquark, our physics maestro

, will help us out with the last one. I have no clue what you are talking about. What does $\displaystyle Hy$

do?