The function f is define for all positive integers n by the

it's clearly that for every prime number p, there're (p-1) numbers from 1 to p-1 which has no common positive factors other than 1 with p.
To make it clearly:
1 and p have only 1 common (+) factor
2 and p have only 1 common (+) factor
.......................................................
(p-1) and p have only 1 common (+) factor.

Look at those provided answer choices:
1)p-2 and (p-1)/2 both are smaller than p-1 ...that means they don't indicate the maximum number of cases which satisfy the problem. ---> eliminate!
2) taking p=2 --> (p+1) is odd ---> (p+1)/2 is not integer ---> unreasonable ---> eliminate this choice
3) also take p=2 ---> f(p) = 1 ----> E can't be the OA

Only A left unbreakable ---> A it is.

OA is A thanks for explaining