The function f(x) performs a Caesar cipher by shifting each character down the alphabet by 3 positions, wrapping back to the start of the alphabet when necessary. It maintains the case of the input characters and does not alter numeric characters.

[CODE]: 
```python
def caesar_cipher(input_string, shift=3):
    result = []
    for char in input_string:
        if char.isalpha():
            offset = 65 if char.isupper() else 97
            result.append(chr(((ord(char) - offset + shift) % 26) + offset))
        else:
            result.append(char)
    return "".join(result)
```