Question

What are the domain and range of g(x)= √x-3?

A. D: [3, ∞) and R: [0, ∞)
B. D: [–3, ∞) and R: [0, ∞)
C. D: (–3, ∞) and R: (–∞, 0)
D. D: (3, ∞) and R: (–∞, 0)

Answer 1

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.