Regardless of the type of hair transplant procedure you have, whether FUE or FUT, the roots from the donor hair are taken from the back side of the head. These hairs are then transplanted into the area(s) which you are seeking coverage, typically the top of your head. Because these hair’s DNA are already resistant to the DHT hormone, once transplanted to the new area(s) they will remain resistant.
Once that hair has been transplanted it is 100% your real hair and will never fall out. You can cut, dye, or shave (but why would you?) and it will grow right back as your natural hair color. While your doctor should cover this, it is highly recommended that once the procedures are completed that you start taking medication to reduce the risk of further losing any other hair in that area which was not transplanted. Those hairs that were not transplanted are still suspect to the DHT hormone and may still fall out.