Consider the following functions. f₁(x) = 8, f₂(x) = cos²(x), f(x) = sin²(x) g(x) = c₁f₁(x) + C₂f₂(x) + C3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞o, co). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {[ {C₁, C₂, C3} = Determine whether f₁, f2, f3 are linearly independent on the interval (-∞o, co). O linearly dependent O linearly independent

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