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

a. The function f(x) = √x has a Taylor series centered at 0.

b. The function f(x) = csc x has a Taylor series centered at π/2.

c. If f has a Taylor series that converges only on (-2, 2), then f(x²) has a Taylor series that also converges only on (-2, 2).

d. If p(x) is the Taylor series for f centered at 0, then p(x - 1) is the Taylor series for f centered at 1.

e. The Taylor series for an even function about 0 has only even powers of x.