Final answer:
The question deals with a simple cryptographic encryption function, where the result f(p) after applying f(p) = (3p + 7) mod 26 yields the encrypted value. This value corresponds to the number associated with a letter in the alphabet after encryption.
Step-by-step explanation:
The student is asking to identify the output (number of pain) from an encryption function given as f(p) = (3p + 7) mod 26. This type of function is often used in simple cryptography, where 'p' would be the plaintext numerical value of a letter, and 'f(p)' would be the ciphertext after applying the function. For example, if we want to encrypt the letter 'A' which corresponds to 0 in the 0-25 range (A=0, B=1, ..., Z=25), we substitute 'p' with 0 and get f(0) = (3×0 + 7) mod 26 = 7. In this case, the encrypted value, or the 'number of pain', is 7, corresponding to the letter 'H'.
To use the encryption function with a different plaintext letter, you would substitute 'p' with the numerical value associated with that letter and apply the function similarly. Always remember to perform the modulo operation at the end, which ensures that the result is within the range of 0-25, representing the letters of the English alphabet.