WASHINGTON — Teeth-bleaching isn’t brain surgery, although the Supreme Court seemed to find a link between the two in an antitrust case argued Tuesday.

Among the questions before the justices is whether it is unfair under federal law for a state regulatory board made up mostly of dentists to prevent lower-cost competitors who aren’t dentists from offering teeth-whitening services.

The outcome could turn on how the justices’ decision affects brain surgeons, lawyers and others whose practices often are regulated by other members of their professions.

The court’s consideration of the dispute between the North Carolina State Board of Dental Examiners and the Federal Trade Commission is being closely watched by the growing number of occupations that require licenses and state supervision, often in the form of boards made up of people in the same businesses and sometimes elected by their peers. The federal appeals court in Richmond, Va., sided with the FTC in ruling that the board engaged in unfair competition.

On Tuesday, several justices worried aloud about discouraging people from serving on these state boards by opening their decisions to second-guessing by the courts. Justice Stephen Breyer was among members of the court who wanted to be sure that, whatever the court decides, it does not take away authority from the people who know best.

He invoked a fictitious board of neurologists to make his point. “We would like this group of brain surgeons to decide who can practice brain surgery in this state. I don’t want a group of bureaucrats deciding that,” Breyer said.