Solution of linearly dependent functions

Question

I'm having a lot of trouble with this question. I know they are not linearly independent, but I'm not sure how to proceed. Here is the problem: Thank you.

Answer 1

It's straightforward to see that $$f-g+2h=0.$$

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Explanation: If $X=e^{3x}$ and $Y=\cos 5x$, you want to find $a,b,c$ such that $$a(X-Y)+b(X+Y)+cY=(a+b)X+(-a+b+c)Y=0.$$ I found $1$, $-1$ and $2$ simply by guessing.