The range of a function refers to the set of all possible output values. To find the range of the given piecewise function g(x), we need to consider the two cases separately:
Case 1: x < 2
In this case, g(x) = x^2 - 5. The graph of this function is a parabola that opens upward and has a vertex at (0,-5). Since the parabola is open upward, the minimum value of g(x) occurs at the vertex and is g(0) = -5. As x increases, g(x) increases without bound. Therefore, the range of g(x) for x < 2 is (-5, ∞).
Case 2: x ≥ 2
In this case, g(x) = 2x. The graph of this function is a line with slope 2 and y-intercept 0. Since the line has a positive slope, g(x) increases as x increases. Therefore, the range of g(x) for x ≥ 2 is [4, ∞).
To find the overall range of g(x), we need to consider the union of the two ranges, which is (-5, ∞).