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If the function f (x) defined on R satisfies f (x) + 2F (- x) = 2x + 1, then f (2)=________
f（x）+2f（-x）=2x+1
Let x = 2
f(2)+2f(-2)=5①
Let x = - 2
f（-2）+2f（2）=-3 ②
② X 2 - 1
3f(2)=-6-5=-11
f(2)=-11/3
The function f (x) whose domain is r satisfies f (x + 1) = 2F (x), and when x ∈ (0,1], f (x) = x2-x, then when x ∈ [- 2, - 1], the minimum value of F (x) is ()
A. -116B. -18C. -14D. 0
When x ∈ [- 2, - 1], x + 2 ∈ [0, 1], ｜ f (x + 2) = (x + 2) 2 - (x + 2) = x2 + 3x + 2, and f (x + 1) = 2F (x), ｜ f (x + 2) = f [(x + 1) + 1] = 2F (x + 1) = 4f (x), ｜ 4f (x) = x2 + 3x + 2 (- 2 ≤ x ≤ - 1), ｜ f (x) = 14 (x2 + 3x + 2) = 14 (x2 + 32) 2-116 (- 2 ≤ x ≤ - 1), ｜ when x = - 32, f (x) gets the minimum value of - 116
RELATED INFORMATIONS
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