And f(P)∩f(M)=(0, positive infinity) is not equal to an empty set, so (1) is incorrect.

However, if P∩M is not equal to an empty set, we can get P∩M={0} from the definition of the function. At this time, f(P)∩f(M) is not equal to an empty set, so (2) is correct.

Similarly, we can take P= and M=(0, positive infinity), or P= (negative infinity, 0] and M=[0, positive infinity), both of which have P∩M=R, so (4) is correct.