Marked-state phase oracle

If $f$ marks only $x_0$, phase kickback realizes $I_{x_0}=I-2|x_0⟩⟨x_0|$ on the search register.

Suppose $U_f$ agrees with the reversible identity-function oracle except at $x_0$, where its answer differs by a fixed one-bit string $a$. Composing $U_f$ with the known identity oracle and preparing the affected answer qubit in $|-⟩$ kicks back the phase $-1$ exactly on $|x_0⟩$, using one query to $U_f$.