Determine whether the following statements are true and give an explanation or counterexample.

a. The interval of convergence of the power series ∑c_k (x - 3)^k could be (-2, 8).

b. The series ∑(-2x)^k converges on the interval -1/2 < x < 1/2.

c. If f(x) = ∑c_k x^k on the interval |x| < 1, then f(x²) = ∑c_k x^2k on the interval |x| < 1.

d. If f(x) = ∑c_k x^k = 0, for all x on an interval (-a, a), then c_k = 0, for all k.