The function f(x) applies the Caesar Cipher technique shifting all alphabet characters 2 positions forward in the English alphabet, preserving the case (upper or lowercase) and also preserving non-alphabet characters and numbers.

[CODE]:
```python
def caesar_cipher(input_str):
    output_str = ""
    for ch in input_str:
        if ch.isalpha():
            shift = 2
            if ch.islower():
                output_str += chr((ord(ch) - ord('a') + shift) % 26 + ord('a'))
            else:
                output_str += chr((ord(ch) - ord('A') + shift) % 26 + ord('A'))
        else:
            output_str += ch
    return output_str
```