The function f(x) appears to shift each alphabetical character in the input string (ignoring the case) by 8 positions forward in the alphabet while wrapping around. Numbers and special characters remain unchanged.

[CODE]:
```python
def shifted_string(input_string):
    result = ""
    for char in input_string:
        if char.isalpha():
            shift_amount = 8
            shifted_char = chr(((ord(char.lower()) - ord('a') + shift_amount) % 26) + ord('a'))
            result += shifted_char
        else:
            result += char
    return result
```