Final answer:
A therapist using confrontation and homework assignments to challenge a client's beliefs is likely a cognitive-behavioral therapist, a directive approach that focuses on changing thought and behavior patterns.
Step-by-step explanation:
The therapist who challenges her client's irrational and self-defeating beliefs using persuasion, confrontation, and homework assignments is likely a cognitive-behavioral therapist. This approach is part of the cognitive-behavioral therapy (CBT) technique, which merges cognitive and behavioral strategies to treat psychological disorders. Unlike client-centered therapy, which is based on the work of Carl Rogers and emphasizes the patient taking a lead role with a therapist who displays unconditional positive regard, genuineness, and empathy, CBT is more directive and involves the therapist actively working with the client to identify and change dysfunctional thinking and behavior patterns.