Final answer:
The stomach's essential life-sustaining function is the production of intrinsic factor, necessary for vitamin B12 absorption, which supports red blood cell formation and neurological health. Thus, the option c is the correct answer.
Step-by-step explanation:
The role of the stomach that is essential to life is the production of intrinsic factor. This substance is critical because without it, the intestinal absorption of vitamin B12 cannot occur. Vitamin B12 is essential for the production of mature red blood cells and for maintaining normal neurological functioning. If someone undergoes a total gastrectomy, they can survive by receiving vitamin B12 injections to compensate for the loss of intrinsic factor production by the stomach.