Let a ∈ R, F & nbsp; (x) = x2 + 2A | X-1 |, X ∈ R. (1) discuss the parity of F & nbsp; (x); (2) find the minimum of F & nbsp; (x)

Let a ∈ R, F & nbsp; (x) = x2 + 2A | X-1 |, X ∈ R. (1) discuss the parity of F & nbsp; (x); (2) find the minimum of F & nbsp; (x)

∵ F & nbsp; (x) = x2 + 2 & nbsp; a | X-1 |, X ∈ R. (1) when a = 0, F & nbsp; (x) = X2, the function is even; when a ≠ 0, the function is not odd or even Because f (1) = 1, f (- 1) = 1 + 4A ≠ f (1), that is, when a ≠ 0, the function is not even (3) when a ≠ - 12, f

Given the function f (x) = 2x & # 178; - 4ax + A, X ∈ [2,4] (1) find the maximum value g (a) (2) find the minimum value H (a)

f(x)=2(x-a)^2+a-2a^2
The axis of symmetry is x = a
If a > 4, then G (a) = f (2) = 8-7a, H (a) = f (4) = 32-15a
If a

If the odd function f (x) is an increasing function in the interval [3,7], the maximum value in the interval [3,6] is 8 and the minimum value is - 1, then 2F (- 6) + F (- 3)=______ ．

F (x) is also an increasing function in the interval [3, 6], that is, f (6) = 8, f (3) = - 1  2F (- 6) + F (- 3) = - 2F (6) - f (3) = - 15, so the answer is: - 15

If the odd function f (x) is an increasing function in the interval [6,1], and the maximum value is 10 and the minimum value is 4,
So is f (x) an increasing or decreasing function on [- 6, - 1]? Find the maximum and minimum of F (x) on [- 6, - 1]

The question is quite simple
Because the property of odd function is symmetric about the origin
So it is also a monotone increasing function on [- 6. - 1]
And because - f (x) = f (- x)
So f (x) max = - f (1) = - 4
f（x）mim=-f（6）=-10
If you don't understand it, just look at the properties of odd functions

If the odd function f (x) is an increasing function in the interval [3,7], the maximum value in the interval [3,6] is 8 and the minimum value is - 1, then 2F (- 6) + F (- 3)=______ ．

F (x) is also an increasing function in the interval [3, 6], that is, f (6) = 8, f (3) = - 1  2F (- 6) + F (- 3) = - 2F (6) - f (3) = - 15, so the answer is: - 15

If the odd function f (x) is an increasing function in the interval [2,9], the maximum value in the interval [3,8] is 9 and the minimum value is 2, then f (- 8) - 2F (- 3) is equal to?

F (x) is an increasing function in the interval [2,9]
Then [3,8] above
The maximum value is f (8) = 9, and the minimum value is f (3) = 2
It's an odd function again
So f (- 8) = - f (8) = - 9, f (- 3) = - f (3) = - 2
Then f (- 8) - 2F (- 3) = - 9-2 × (- 2) = - 5

Given that a and B are reciprocal and m and N are opposite, the value of 12ab − 3M − 3N is______ ．

∵ A and B are reciprocal, ∵ AB = 1, ∵ m and N are opposite, ∵ m + n = 0, ∵ 12ab-3m-3n = 12ab-3 (M + n) = 12 × 1-3 × 0 = 12

Given that a and B are reciprocal and m and N are opposite, what is the value of 1 / 2Ab + 3M + 3N?

From the meaning of the title:
ab=1
m+n=0
So:
1/2ab+3m+3n
=1 / 2 × 1 + 3 (M + n)
=1 / 2 + 3 × 0
=1 / 2

Given that m and N are opposite to each other, C and D are reciprocal to each other, and the distance from a to the origin is 1, find the value of 3M + 3N + 2CD + a

∵ m, n are opposite numbers to each other, ∵ m + n = 0, ∵ C, D are reciprocal numbers to each other, ∵ CD = 1, ∵ A's distance to the origin is 1, ∵ a = ± 1, a = 1, 3M + 3N + 2CD + a = 3 (m + n) + 2CD + a = 0 + 2 + 1 = 3, a = - 1, 3M + 3N + 2CD + a = 3 (M + n) + 2CD + a = 0 + 2-1 = 1, so the value of 3M + 3N + 2CD + A is 3 or 1

If X & # 178; = 9, m and N are opposite to each other, and a and B are reciprocal to each other, then 3M + 3n-2ab - 4 / x =?

That is, x = ± 3
m+n=0
ab=1
So the original formula is 3 (M + n) - 2ab-4 / X
=3*0-2*1-4/x
=-2-4/x
=-2-4 / (- 3) = - 2 / 3 or = - 2-4 / 3 = - 10 / 3