Which statement best describes the domain and range of f(x) = –(7)x and g(x) = 7x?
f(x) and g(x) have the same domain and the same range.
f(x) and g(x) have the same domain but different ranges.
f(x) and g(x) have different domains but the same range.
f(x) and g(x) have different domains and different ranges.

Given:

The two functions are and

We need to determine the statement that describes the domain and range of these two functions.

Domain and range of the function :

Domain is the set of all independent x - values for which the function is real and well defined.

Since, the function has no undefined points, the domain of the function is

Range is the set of all dependent y - values for which the function is well defined.

The range of the exponential function is of the form is

Thus,

Hence, the range of the function is

Domain and range of the function :

The function has no undefined points and hence, the domain of the function is

The range of the exponential function is of the form is

Thus,

Hence, the range of the function is

Thus, from the functions f(x) and g(x) have the same domain but different ranges.

Hence, Option B is the correct answer.