The function replaces the first character of the string with the next character in the ASCII character set if it is a consonant.

[CODE]:
```python
def f(x):
    vowels = ['a', 'e', 'i', 'o', 'u']
    
    if x[0] not in vowels:
        first_char_ascii = ord(x[0])
        next_char_ascii = first_char_ascii + 1
        next_char = chr(next_char_ascii)
        return next_char + x[1:]    
    else:
        return x
```

This code checks whether the first character of the string is a vowel or a consonant. If it's a consonant, it replaces it with the next character in the ASCII character set and returns the modified string. Otherwise, it returns the input string unchanged.