The function f(x) appears to be a simple substitution cipher that replaces each letter in the input string with a corresponding letter a fixed number of positions down the alphabet. For example, the input string "apple" is replaced with the output string "elppa" because the letter "a" is moved 3 positions down the alphabet to become the letter "e". Similarly, the input string "banana" is replaced with the output string "ananab" because the letter "a" is moved 2 positions down the alphabet to become the letter "n", and the letter "n" is moved 1 position down the alphabet to become the letter "a".

