The function takes a string input and shifts each character backward in the alphabet by a number of positions equal to the position of that character in the alphabet. If the result goes beyond 'a', it wraps around to 'z'.

[CODE]: 
```python
def f_approx(x):
    result = ""
    for c in x:
        position = ord(c) - ord('a') + 1
        shifted_c = chr(((ord(c) - ord('a') - position) % 26) + ord('a'))
        result += shifted_c
    return result
```