The domain of the function is all real numbers except for the interval [-128, -32]. In this interval, the function is undefined (nan). 

[CODE]:
```python
def f(x):
    if -128 <= x <= -32:
        return "Undefined"
    elif x == 0:
        return float('inf')
    elif 32 <= x <= 128:
        # Replace the following line with the actual calculation based on the function implementation
        return -1 * x  # Example code assumes the function returns negative values in this range
    else:
        return "Invalid input"
```
Note: The code provided is a placeholder and needs to be replaced with the actual code implementing the function.