The function takes an input string and iterates through its characters. If the character is a letter, it converts it to its corresponding position from the end of the alphabet and inverts its case; for example 'a' becomes 'Z', 'A' becomes 'z', 'b' becomes '{', and 'B' becomes '['. The function appears to ignore digits and special characters, which remain unchanged.

[CODE]: 
```python
def f(x):
    result = ''
    for char in x:
        if char.isalpha():
            inverted = chr(219 - ord(char))
            result += inverted.swapcase()
        else:
            result += char
    return result
```