The domain of the function is all numerical values between -128 and 128. The function displays unexpected behavior for the input value of 0, where it returns None. 

[CODE]:
```python
def f(x):
    if x == 0:
        return None
    elif -5 <= x <= 5:
        # Replace this line with the code that computes the output for this range of inputs
        return <numerical computation>
    else:
        # Handle other input values here (optional)
        return <output for other input values>
```

Please note that the above code is a rough approximation and only accounts for the observed behavior. The actual implementation of the function may involve more complex calculations or considerations.