The known function f (x) = [3x2-4, x > 0; π, x = 0; 0, X

The known function f (x) = [3x2-4, x > 0; π, x = 0; 0, X

f(1)=3*1^2-4=-1
f(2)=3*2^2-4=8>0 => f[f(2)]=f(8)=3*8^2-4=188
a> When f (a + 1) = 3 (a + 1) ^ 2-4 = 3A ^ 2 + 6A + 2
When a = - 1, f (a + 1) = f (0) = Pai
a

Given the function f (x) = kx3-3x2 + 1 (K ≥ 0); (I) find the monotone interval of function f (x); (II) if the minimum value of function f (x) is greater than 0, find the value range of K

(1) When k = 0, the monotone increasing interval of F (x) = - 3x2 + 1  f (x) is (- ∞, 0), and the monotone decreasing interval is [0, + ∞). When k > 0, the monotone increasing interval of F '(x) = 3kx2-6x = 3kx (x-2k) ‖ f (x) is (- ∞, 0], [2K, + ∞), and the monotone decreasing interval is [0, 2K]. (II) when k = 0, the function f (x) has no minimum value. When k > 0, according to the meaning of the problem, f (2k) = 8k2-12k2 + 1 K > 0, that is, K2 > 4, from the condition k > 0, so the value range of K is (2, + ∞)

The monotone increasing interval of function f (x) = A-B ^ (3x ^ 2-5x-2) is
b>1

f(x)=a-b^(3x^2-5x-2)
∵b＞1
When 3x ^ 2-5x-2 decreases monotonically, B ^ (3x ^ 2-5x-2) decreases monotonically, and f (x) = A-B ^ (3x ^ 2-5x-2) increases monotonically
Also: G (x) = 3x ^ 2-5x-2, opening upward, axis of symmetry x = - (- 5) / (2 * 3) = 5 / 6
When x < 5 / 6, B ^ (3x ^ 2-5x-2) decreases monotonically
The monotone increasing interval f (x) = A-B ^ (3x ^ 2-5x-2) is (- ∞, 5 / 6)

1. Let f (2 / x) = x / x + 2, then f (x-1) =? 2?

F (x-1) = 1 / X; monotone interval is (- ∞, 1) monotone increasing, [1,5] monotone decreasing, [5, + ∞)