The function f(x) takes an input string, keeps the first character unchanged if it's a digit, symbol or an empty string, otherwise, it substitutes the first character with a character 20 positions ahead in the ASCII table, and appends an 'x' to the end of the string.

[CODE]:
```python
def f(x):
    if len(x) == 0 or not x[0].isalpha():
        return x + 'x'
    else:
        return chr(ord(x[0]) + 20) + x[1:] + 'x'
```

Please let me know if you want to test more inputs or you're satisfied with this description and implementation.