Let f g:-1, 1]> r, fx)=x, gr) = x|x| then fand g are linearly independent on [-1, 1} fand g are linearly dependent on [-1, 1] ac) f) g(x)-f) gtr) is not identic

Let f g:-1, 1]> R, fx)=x, gr) = x|x| Then fand g are linearly independent on [-1, 1} fand g are linearly dependent on [-1, 1] Ac) f) g(x)-f) gtr) is NOT Identically zero on [-1, 1] There exist continuous function p(x) and q(x) such that fandg satisfy +py + qy = 0 on -1, 4