The domain of the function includes all numerical values. However, the function behaves unexpectedly for negative inputs, where it is undefined or returns NaN. It is important to note that the behavior of the function is well-defined for positive inputs and 0.

[CODE]:

def f(x):
    if x < 0:
        return float('nan')
    elif x == 0:
        return float('inf')
    else:
        return 1.7

This Python code approximates the behavior of the function described above.