Construct a g∈Cc[infinity](ℝⁿ) such that g(x) = g(|x|) and g(x) ≥ 0 with g(x) = 0 whenever |x| ≥ 1. Which of the following properties does the function g possess?

a) g(x) is always negative.
b) g(x) is equal to zero for all x.
c) g(x) is non-negative and symmetric with respect to |x|.
d) g(x) is only defined for x ≥ 1.