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1. Given that f (x + 2) = 4x ^ 2 + 4x + 3 (x belongs to R), then the range of function f (x) is]
t=x+2,f(t)=4t^2-12t+11,min=2
Given f (x) = (4x ^ 2-7) / (2-x) 0 ≤ x ≤ 1, find the monotone interval and range of F (x)
Don't change the element, use the formula of derivative
Let 2-x = t, 1 ≤ t ≤ 2, f (T) = (4 * (2-T) ^ 2-7) / T = 4T + 9 / t-16. When 4T = 9 / T, t = 1.5, then x = 0.5 x ∈ [0,0.5] decreases, (0.5,1] increases, f (0) = - 3.5, f (1) = - 3, f (0.5) = - 4 range is [- 4, - 3] f '(x) = (8x (2-x) + (4x ^ 2-7)) / (X-2) ^ 2. Let f' (x) = 0 get
F (x) = Log1 / 2 (- x + 4x-3)?
Negative infinity ~ Log1 / 2
The value range of a function can not be separated from the definition range of a function. For example, the maximum value of this problem (- x + 4x-3) is 1
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