# Which of these functions are linearly independent?

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.

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All but 2. are linearly independent. The second pair of functions is linearly dependent, as $$g(x)=e^{3(x-3)}=e^{3x-9}=e^{-9}e^{3x}=e^{-9}f(x)$$ so $e^{-9}f(x)+(-1)g(x)=0$.