one one and onto

I think answer shud be B)
f(0) = f(∩) = 0 hence not a one one function
further range of 2 + cos²x is (2,3) and that of the other function is R
Range of the other function can be calculated by considering two cases
CASE 1- x<∩
CASE 2- x>∩

Since either case 1 OR case 2 is possible we use union in combining the ranges

What is the answer given?????

ayush i too got the same answer but via graphs