The function f(x) takes an input string and increments the ASCII value of every second character by 2 if it is an alphabetic character, while keeping all other characters unchanged. The ASCII value wraps around from 'z' to 'a' and from 'Z' to 'A' when incremented.

[CODE]: 
```python
def approximate_f(x):
    output = []
    for i, char in enumerate(x):
        if char.isalpha() and i % 2 == 1:
            if char == 'z':
                output.append('a')
            elif char == 'Z':
                output.append('A')
            else:
                output.append(chr(ord(char) + 2))
        else:
            output.append(char)
    return ''.join(output)
```