Consider the following functions. f₁(x) = x₁ f₂(x) = x², f3(x) = 2x - 3x² 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} = Determine whether f₁, f₂, f3 are linearly independent on the interval (-∞, ∞). O linearly dependent O linearly independent

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Q: Find a function f(x) so that h(x) = (gof)(x) given that -2x³ – 6x² 6x² + 5x+1 and g(x): = h(x) =…

A: (g∘f)(x) = g(f(x))

Q: = Solvex (t) = Ax(t) where A 3 -2 [1] [8] = 4 and (0)

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Q: A homogeneous second-order linear differential equation, two functions y₁ and y₂, and a pair of…

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Q: 8. Let f(x) = -x-2, g(x) = 4x + 1, h(x) = 2(x − 3) +1 (a) Evaluate h(-2) (b) Evaluate f(0) (c) Solve…

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Q: Determine at what point(s) the graphs of f(x) = /2r+6 and g(z) = vAz – 8 intersect. Let f(z) = (10r…

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