The function shifts the first character of the input string by one step forward in the alphabet and keeps the rest of the string unchanged. Lowercase letters are replaced by the next lowercase letter, and uppercase letters are replaced by the next uppercase letter. If the first character is a "z" or "Z", it is changed to "a" or "A", respectively. Special characters and digits are left untouched.

[CODE]: 

```python
def fx(input_string):
    if not input_string:
        return input_string
      
    first_char = input_string[0]
    if first_char.isalpha():
        next_char = chr(((ord(first_char.upper()) - 65 + 1) % 26) + 65)
        if first_char.islower():
            next_char = next_char.lower()
    else:
        next_char = first_char
        
    return next_char + input_string[1:]
```