The function reverses the input string and applies a Caesar cipher shift on the first character. The Caesar cipher shift rotates the first character towards the beginning of the alphabet it belongs to (alphabetic or numeric) by a fixed number of positions. The shift appears to be 3 positions for alphabetic characters and 4 positions for numeric characters.

[CODE]:
```python
def f(x):
    reversed_x = x[::-1]
    first_char = reversed_x[0]
    
    if first_char.isalpha():
        if first_char.islower():
            shifted_char = chr(((ord(first_char) - ord('a') - 3) % 26) + ord('a'))
        else:
            shifted_char = chr(((ord(first_char) - ord('A') - 3) % 26) + ord('A'))
    elif first_char.isdigit():
        shifted_char = chr(((ord(first_char) - ord('0') - 4) % 10) + ord('0'))
    else:
        shifted_char = first_char
    
    result = shifted_char + reversed_x[1:]
    return result
```
Please note that this code may not be an exact match with the original implementation, but it approximates the observed behavior of the function.