The radiation itself disappears immediately. There is both cellular death and cellular damage caused by even a single x-ray. That is also the case when one flies at a high altitude in an aircraft. The damage does not"disappear". The damage is caused by the energy from the pulse as well as the free radicals generated by the energy. There is no such thing as a "harmless" x-ray. Mother nature causes new cell structures to develop. The problem is when the DNA is damaged by the x-ray and an imperfect replication occurs, or when the telomeres are damaged. Your question seems to be "is there anything to fear from an x-ray". The answer is that there is more to fear from not being able to make a diagnosis. This is all risk-benefit. X-rays should be avoided whenever necessary. Many hospitals insist on a full set of chest x-rays simply to cover themselves in the event of legal difficulties. Ask about the reason for every x-ray and don't be afraid to refuse unnecessary x-rays and to request a lead shield for the parts of your body not being filmed.
No, it does give you a dose of radiation for a short time but that goes away after a few months.
You have posted this identical question in several forums. All x-rays cause damage to cells as they pass through the body. There is no such thing as a "safe" x-ray. This damage is cumulative. Nevertheless, x-rays are necessary for the diagnosis of many problems that would otherwise cause death, so this is a risk-benefit decision. The radiation breaks links in chains of DNA and destroys structures within the cells. This damage sometimes interfere with their ability to replicate normally, and in some cases can cause a malignancy.