Final answer:
The inverse of the function g(x) = x^2 - 4 is not a function as it fails the Horizontal Line Test, where horizontal lines intersect the graph in more than one point.
Step-by-step explanation:
To determine if the inverse of the function g(x) = x^2 - 4 is a function, we can use the Horizontal Line Test. This test involves drawing horizontal lines across the graph of the function; if any horizontal line intersects the graph at more than one point, then the inverse of the function is not a function because it would not pass the Vertical Line Test, which is a requirement for a relation to be a function.
The function g(x) = x^2 - 4 is a parabola opening upwards. A horizontal line drawn at any y-value greater than -4 will intersect the parabola at two different x-values. This means that the inverse of this function does not pass the Horizontal Line Test, and thus the inverse is not a function.