Problem #2: Which of the following sets of functions are linearly independent on the interval (-?, ?)?
(i) $f_1(x) = 4 + x$, $f_2(x) = 5x^2$, $f_3(x) = x^2 + 7$
(ii) $f_1(x) = e^{6x}$, $f_2(x) = 9e^{3x}$, $f_3(x) = 5e^{8x}$
(iii) $f_1(x) = 7sin^2x$, $f_2(x) = 6cos 2x$, $f_3(x) = 9$
(A) (i) and (ii) only (B) (ii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) (iii) only (F) all of them
(G) (i) only (H) none of them