The implicit domain of f would be all real numbers other than 2. With this domain statement, the function is given a continuous domain on an open interval between -∞ and P. If P were greater than 2, there would be a conflict, because the interval would include a discontinuity at 2.
P ≤ 2
The limit P can equal 2, and the open domain interval would still exclude 2. However, P might otherwise be number less than 2, and there still would be no conflict.