The function f(x) receives an input string and increments each alphabetical character by 20 positions (wrapping around when needed). Non-alphabetical characters remain unchanged in the output.

[CODE]: 
```python
def f_approx(x):
    output = ""
    for char in x:
        if char.isalpha():
            if char.islower():
                output += chr(((ord(char) - ord('a') + 20) % 26) + ord('a'))
            else:
                output += chr(((ord(char) - ord('A') + 20) % 26) + ord('A'))
        else:
            output += char
    return output
```