A project manager receives a serious complaint from a functional manager about a team member. What should the project manager do?

The project manager should first discuss the issue with the functional manager to understand the specific nature and validity of the complaint. This allows for gathering facts and context before taking any action. Without understanding the complaint, any other action would be premature and potentially detrimental. Supporting the team member without understanding the complaint could escalate the conflict if the complaint is valid. Replacing the team member immediately is an extreme measure that could harm project progress and team morale without proper investigation. Protecting the team member and involving the sponsor without understanding the complaint is also premature and bypasses the direct communication needed to resolve the issue.