Final answer:
In the given sentence, the relative pronouns that introduce nonessential dependent clauses are 'who' in both parts (a) and (b). They link additional, nonessential information about their antecedents 'the officer' and 'Dr. Rathbone', respectively.
Step-by-step explanation:
In the sentence, 'She is the officer (a) who hired me, but Dr. Rathbone, (b) who is her boss, gave me a good recommendation', the designated relative pronouns that introduce nonessential dependent clauses are both 'who' in parts marked (a) and (b).
Relative pronouns introduce clauses and refer back to a noun or pronoun in the sentence known as the antecedent. Here, the antecedents for both instances of 'who' are 'the officer' and 'Dr. Rathbone', respectively. The relative pronouns are connecting additional information about these entities.
Remember that relative pronouns serve to provide extra information to the sentence that can often be removed without changing its overall meaning. Hence, they are called nonessential dependent clauses.
Learn more about Relative Pronouns