Final answer:
The cathode supplies and controls the heat required by the x-ray tube filament for thermionic emission of electrons, leading to the production of x-ray photons.
Step-by-step explanation:
The component that supplies and controls the heat required by the x-ray tube filament for thermionic emission of electrons is the cathode. Electrons are emitted from a hot filament when they are thermionically agitated. Then, these electrons are accelerated by a high voltage towards the anode, where their kinetic energy is transformed into x-ray photons upon collision.
While the rectifier ensures the current flow is in one direction and the autotransformer adjusts the incoming voltage, it is the cathode's specific responsibility to heat and emit electrons through the filament. The anode's role, however, is to serve as a target for the electrons and not to control the filament’s temperature. Therefore, the correct answer is (b) Cathode.