Answer:
The answer wound be C. {-6, -5, -4, 4, 5, 6}.
Explanation:
For g(x) = 1:
|x| - 3 = 1
|x| = 4
The equation |x| = 4 has two solutions: x = 4 and x = -4.
For g(x) = 2:
|x| - 3 = 2
|x| = 5
The equation |x| = 5 has two solutions: x = 5 and x = -5.
For g(x) = 3:
|x| - 3 = 3
|x| = 6
The equation |x| = 6 has two solutions: x = 6 and x = -6.
Now, we have six possible values for x: 4, -4, 5, -5, 6, and -6. Therefore, the domain of g(x) = |x| - 3, given that the range is {1, 2, 3}, is {-6, -5, -4, 4, 5, 6}.