I am so lost on this question I am not sure even where to start. I am not looking for an answer but more of a turn in the right direction.
Find all the eigenvalues and eigenfunctions of the following linear transformation: $T(f(x)) = f(-x)$ from $\mathbf{P}_2$ to $\mathbf{P}_2$. IS T diagonalizable?
All I know for sure is that the standard basis is $1$, $x$, $x^2$, and if this is an eigenbasis for $T$ then $T$ is diagonalizable.
Thanks for any assistance!