The domain of a function is the interval containing all the values for which the function is well defined. Since this is not a rational function, i.e., it's not a fraction of polynomials, the function is well defined for all values of x. Therefore, the domain is:
Domain: (-∞, ∞)
Now, in order to find the range, we need to notice that x² is always positive or zero. Therefore, we have:
x² ≥ 0
(1/2)x² ≥ 0
(1/2)x² + 5 ≥ 0 + 5
(1/2)x² + 5 ≥ 5
g(x) ≥ 5
Thus, the range of the function is all the values greater than or equal to 5:
Range: [5, ∞)