It looks to me like they are all linearly independent but that is coming back as incorrect.
What is the general procedure for doing this anyway, I presume it is setting $c_1f(x) + c_2g(x) = 0$ and trying to find out if there are any non trivial solutions for c1 and c2...that is what I did but in every case I found c1 and c2 to be zero.