The function f(x) performs a Caesar cipher encoding on the input string with a fixed shift of 15 characters. It keeps the case of the input characters unchanged.

[CODE]:
```python
def caesar_cipher(text, shift=15):
    result = ""

    for char in text:
        if char.isalpha():
            shift_amount = 65 if char.isupper() else 97
            result += chr(((ord(char) - shift_amount + shift) % 26) + shift_amount)
        else:
            result += char

    return result
```

Please let me know if you want to run additional tests or need further clarification.