Question

What are the domain and range of the real-valued function f(x)=2/x?

Select one:
a. The domain is all real numbers except 0. The range is all real numbers except 0. b. The domain and the range are all real numbers.
c. The domain is x>0. The range is f(x)>0.
d. The domain is all real numbers except 0. The range is all real numbers.

Answer 1

For this case we have the following function:
 f (x) = 2 / x
 We note that the denominator of the function is not defined for:
 x = 0
 Thus,
 the domain is all the real distintios of zero.
 the range is all the real distints of zero. 
 Answer:
 a. The domain is all real numbers except 0. The range is all real numbers except 0.

Answer 2

The domain of a function is the set of all possible values of dependent variable. 
The range of a function is the set of all possible results. 

In the case above, the domain of f(x)=2/x? is all real numbers of x except 0.
The range of f(x)=2/x? is the set all real numbers except 0.

∴ From the choices, the given the answer is,
a. The domain is all real numbers except 0. The range is all real numbers except 0