Given:
The two functions are:


To find:
The correct statement about the function  .
.
Solution:
We have,


Adding both functions, we get



It is a quadratic function. So, option A is incorrect and option B is correct.
The domain of  is all real numbers because it is defined for all real values of x. So, option C is incorrect.
 is all real numbers because it is defined for all real values of x. So, option C is incorrect.
The range of  cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.
 cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.
Therefore, the correct option is B.