Final answer:
A dental assistant is typically permitted to take X-rays under direct supervision, which is the correct duty from the given options. Tasks like administering anesthesia, performing complex procedures, or placing fillings independently are not within the scope of a dental assistant's duties.
Step-by-step explanation:
Under direct supervision, a dental assistant is typically permitted to perform tasks such as taking x-rays, assisting the dentist during procedures, preparing materials and tools, and maintaining patient records. Of the options provided, the duty that a dental assistant is allowed to perform under direct supervision is taking X-rays without supervision. However, this might vary by jurisdiction, with some areas requiring the presence of a dentist or a qualified professional for supervision during x-ray procedures.
Administering local anesthesia, conducting complex dental procedures, and placing dental fillings independently are typically beyond the scope of practice for dental assistants, and are usually performed by dentists or specialists with advanced training.