Final answer:
The C7 nerve root is responsible for the middle finger sensation, the C7 and C8 nerve roots are involved in the triceps reflex, and the C6, C7, and C8 nerve roots are involved in thumb extension through the posterior interosseous branch of the radial nerve.
Step-by-step explanation:
The nerve root responsible for middle finger sensation is usually the C7 nerve root because the middle finger is the dermatomal distribution for that nerve root. The triceps reflex is typically mediated through the C7 and C8 nerve roots; when testing this reflex, one can assume that these nerve roots are intact if the reflex is normal. The action of thumb extension is chiefly facilitated by the posterior interosseous branch of the radial nerve, which has its nerve root origins at C6, C7, and C8.
In the case of any neurological issues such as compression of the median nerve, which could lead to carpal tunnel syndrome, these specific nerve root functions could be affected, leading to symptoms such as pain, numbness, or weakness in the relevant dermatomal or myotomal distribution.