The domain of the function is the set of all real numbers. However, there seems to be an unexpected behavior at x = 0, where the output becomes infinity.

[CODE]:

```python
def f(x):
    if x == 0:
        return float('inf')
    else:
        return -abs(x)
```

Please note that this code is an approximation based on the limited information we have obtained from the function f(x).