Do family physicians have a duty to check the functionality of the vital organs of patients?

Yes: If there's a strong family history of any serious medical condition e.G heart attack, diabetes, high cholesterol, cancer, it's worth mentioning to your primary doctor and be pro-active about this so he/she can order regular blood testing or diagnostic work-up specific for a particular body system. Be frank and mention to your doctor of any lingering symptoms so appropriate work-up can be done.