Which of the following duties may NOT be delegated by a dentist?

Taking final impressions for a dental appliance is a duty that typically requires the expertise and judgment of a licensed dentist. This procedure often involves making precise assessments of a patient's specific dental and anatomical needs, which is fundamental for ensuring that the dental appliance fits correctly and functions as intended. The final impression can have significant implications for patient care, and thus, the dentist's direct involvement is necessary to uphold standards of quality and safety in dental practice.

In contrast, the other duties listed, such as polishing teeth, administering nitrous oxide, and taking dental radiographs, can often be delegated with appropriate training and under certain conditions. These tasks do not generally require the same level of clinical judgment as taking final impressions and can be performed by dental assistants or hygienists who have received the necessary training and are operating under the supervision of a licensed dentist.