Which of these subsets of the space of real-valued functions of one real variable is linearly dependent and which is linearly independent? (We have abbreviated some constant functions, e.g., in the first item, the '2' stands for the constant function f(x) = 2.)
(a) {2, 4 sin2(x), cos2(x)}
(b) {1, sin(x), sin(2x)}
(c) {x, cos(x)}
(d) {(1 + x)2, x2 + 2x, 3}
(e) {cos(2x), sin2(x), cos2(x)}
(f) {0, x, x2}