The domain of the function appears to be the entire range of real numbers. However, there seems to be an interval where the function displays unexpected behavior. That interval is [-10, 10]. Within this interval, the function has a rapid increase in growth and exhibits highly oscillatory behavior.

[CODE APPROXIMATION]: Based on the experiments, the following Python code approximates the behavior of the function f(x):

```python
import math

def f(x):
    if -10 <= x <= 10:
        return math.sin(x) + math.cos(x) * (x ** 2 - 5)
    else:
        return x ** 3 + 0.5 * x - 2
```

Please note that this is just an approximation based on the experiments. The actual implementation of the function might involve more complex operations or structures.