F (x) = ax + BX + 1 (a, B ∈ R) if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression of F (x) is obtained F (x) = ax + BX + 1 (a, B ∈ R) ① if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression for finding f (x) holds. ② under the condition of ①, when x ∈ [- 2,2], G (x) = f (x) - KX is a monotone increasing function, the value range of real number k can be found

F (x) = ax + BX + 1 (a, B ∈ R) if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression of F (x) is obtained F (x) = ax + BX + 1 (a, B ∈ R) ① if f (- 1) = 0 and f (x) ≥ 0 for any real number x, the expression for finding f (x) holds. ② under the condition of ①, when x ∈ [- 2,2], G (x) = f (x) - KX is a monotone increasing function, the value range of real number k can be found

F (- 1) = 0, A-B + 1 = 0, A-B = - 1, f (0) = 1 - B / 2A = - 1, B = 2, a = 1, f (x) = x + 2x + 1, the range of F (x) on [- 2,2] is [0,9]