Show that $\phi$ and $\psi$ are not equivalent.
It is enough for the equality to fail at one $f$. You can take $f$ to be the identity, and that's the point of part a), as the problem becomes to show that $T$ and $S$ are not unitarily equivalent. For this, take any rational $\lambda$ and show that it is an eigenvalue for $S$ but not for $T$.