12. Which of the following subsets of is the largest possible domain for the real-valued function (x2 x)1/2?

A.

B.

C.

D.

E.

 

Solution: The answer is D

 

Set the argument of the real-valued function equal to zero and solve for x, as follows.

Let the solution(s) divide the real number line into subsets. Evaluate the argument by one representative of each subset to determine the sign, i.e. positive or negative, of the argument within the entire subset. As the following graph, illustrates:

Since the argument needs to be greater than or equal to zero in order for the function to be real valued, then the largest domain for the given function is,