The function f(x) takes a string input and shifts each English letter by a certain amount, with uppercase and lowercase letters considered separately, while other characters are unchanged. For uppercase letters, the shift amount is -5, and for lowercase letters, the shift amount is +4.

[CODE]: 
```python
def f(x):
    result = ""
    for char in x:
        if 'A' <= char <= 'Z':
            result += chr(((ord(char) - ord('A') - 5) % 26) + ord('A'))
        elif 'a' <= char <= 'z':
            result += chr(((ord(char) - ord('a') + 4) % 26) + ord('a'))
        else:
            result += char
    return result
```

Please note that while this code approximates the behavior of the function, there could be edge cases or discrepancies that require additional exploration.