The function implemented by f(x) removes any non-alphabetic characters from the input string and converts all alphabetic characters to lowercase.

[CODE]:
```python
def f(x):
    # Remove non-alphabetic characters
    alphanumeric = ''.join(c for c in x if c.isalpha())

    # Convert alphabetic characters to lowercase
    transformed = alphanumeric.lower()

    return transformed
```

You can use this code to approximate the behavior of the function implemented by f(x).