Consider the following functions. f₁(x) = 0, f₂(x) = x, f3(x) = ex g(x) = c₁f₁(x) + C₂f₂(x) + C3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution (0, 0, 0}.) {C₁, C₂, C3} = { [

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