The function f(x) takes a string input and returns the input string with each alphabetic character (lowercase and uppercase) shifted by two in the alphabet (cyclically), and removes any numeric characters from the string.

[CODE]:
```python
def approximate_f(x):
    output = []
    for char in x:
        if char.isalpha():
            if char.islower():
                output.append(chr(((ord(char) - ord('a') + 2) % 26) + ord('a')))
            elif char.isupper():
                output.append(chr(((ord(char) - ord('A') + 2) % 26) + ord('A')))
        elif not char.isdigit():
            output.append(char)
    return ''.join(output)
```
