If f (x) = AX2 + BX (a ≠ 0) satisfies 1 ≤ f (- 1) ≤ 2, 2 ≤ f (1) ≤ 5, then the value range of F (- 3) is______ ．

∵ f (x) = AX2 + BX, ∵ f (- 1) = A-B, f (1) = a + B, from which we can get the inequality system 1 ≤ f (− 1) ≤ 22 ≤ f (1) ≤ 5, that is, 1 ≤ a − B ≤ 22 ≤ a + B ≤ 5. Let f (- 3) = λ f (- 1) + μ f (1), we can get 9a-3b = λ (a-b) + μ (a + b) ∵ λ + μ = 9 − λ + μ = - 3, and the solution is λ = 6 μ = 3

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