I know the translation operator behaves as follows:
$$T(a) |x \rangle = |x+a \rangle$$
However my notes state that for a general quantum state $|\psi \rangle$ we know that
$$\langle x| T(a) | \psi \rangle = \psi(x-a)$$
However I am unsure where this comes from and would like to know how to derive this. I know that we can write that $$ \langle x| \psi \rangle = \psi(x)$$ but am unsure what exactly I should do.