Final answer:
The nurse manager is performing the leadership task of advocacy by presenting an in-service on preventing re-admissions following joint arthroplasty.
Step-by-step explanation:
The nurse manager who is presenting an in-service about preventing re-admission of clients due to complications following joint arthroplasty is performing the leadership task of advocacy. Advocacy in healthcare involves supporting clients to ensure that they receive appropriate care, which could prevent complications and subsequent re-admissions. By educating staff on how to better care for patients post-arthroplasty, the nurse manager is advocating for patient well-being and aiming to improve patient outcomes.