The function f(x) takes an input string and shifts the lowercase letters of the alphabet by 1 position backwards. Numbers and uppercase letters remain unchanged.

[CODE]: 
```python
def f_approx(x):
    result = []
    for char in x:
        if 'b' <= char <= 'z':
            new_char = chr(ord(char) - 1)
        elif char == 'a':
            new_char = 'z'
        else:
            new_char = char
        result.append(new_char)
    return ''.join(result)
```
Let's test some edge cases.

COMMAND: PYTHON(./temp/function.py "0!@&*" "abcxyz" "#$%^" "YyZz" " ")