The function f(x) takes string input and applies a Caesar cipher with a shift of 8. It keeps numbers and symbols unchanged and is case-insensitive.

[CODE]:
```python
def caesar_cipher(s, shift=8):
    final_str = ""
    for char in s:
        if char.isalpha():
            start = ord('A') if char.isupper() else ord('a')
            final_str += chr((ord(char) - start + shift) % 26 + start)
        else:
            final_str += char
    return final_str
```

Using this approximate implementation, we can expect the same behavior as the original function f(x) for most of the inputs.