It is known that f (x) is an odd function on R, and when x > 0, f (x) = - x ^ 2 + 2x + 2 Finding the analytic expression of F (x)

It is known that f (x) is an odd function on R, and when x > 0, f (x) = - x ^ 2 + 2x + 2 Finding the analytic expression of F (x)

If x > 0, f (x) = - X & sup2; + 2x + 2, ∫ f (- x) = - (- x) & sup2; + 2 (- x) + 2 = - X & sup2; - 2x + 2, and f (x) is an odd function on R, ∫ f (x) = - f (- x) = x & sup2; + 2x-2, that is, if x0); 0, (x = 0); X & sup2; + 2x-2, (x

Given the function f (x) = A-1 / (2x + 1), if f (x) is an odd function, then a=
That 2x is to the x power of 2, and the answer comes with a reason

For odd functions, then f (0) = 0
0 times of 2 = 1
So A-1 / 2 = 0
a=1/2

It is known that f (x) is an odd function defined on R. when x ≥ 0, f (x) = x ^ 2-2x, then if x ∈ [- 3,0], the range of F (x) is obtained

If x ≥ 0, f (x) = x ^ 2-2x, if x = 0, then f (- x) = (- x) ^ 2-2 * (- x) = x ^ 2 + 2x, because f (x) is an odd function defined on R, then f (- x) = - f (x) = x ^ 2 + 2xf (x) = - x ^ 2-2x, so f (x) = - (x ^ 2 + 2x + 1) + 1 = - (x + 1) ^ 2 + 1 when x ∈ [- 3,0], because the axis of symmetry is x = - 1 | - 3 - (- 1) | = 2 | 0 + 1 | = 1-3

Is there a number whose reciprocal is 1 different from it
The solution is (x + 1) x = 1

(x+1)x=1
x^2+X-1=0
(x+1/2)^2=5/4
X + 1 / 2 = radical 5 / 2 or negative radical 5 / 2
X = (radical 5-1) / 2 or - (radical 5 + 1) / 2

Solve the equations: 5x + 5y-8z = 13 6x + 4y-z = 9 2x + 3y-4z = 5

5x+5y-8z=13 (1)
6x+4y-z=9 (2)
2x+3y-4z=5 (3)
(1)-(3)×2
x-y=3 (4)
(2)×4-(3)
22x+13y=31 (5)
(4)×13+(5)
35x=70
therefore
x=2
y=x-3=-1
z=6x+4y-9=-1

In the graph of the following functions, the one whose zeros cannot be solved by dichotomy is ()
A. B. C. D.

For a function that can find the zero point of a function by dichotomy, the sign of the function value on the left and right sides of the zero point is opposite, which can be obtained from the image. Only C can not satisfy this condition, so C is selected

As shown in the figure, it is known that the parabola y = x2 + BX + C passes through the point (0, - 3). Please determine the value of B so that the intersection of the parabola and the X axis is between (1,0) and (3,0). The value of B you determine is______ ．

Substituting (0, - 3) into the analytical formula of the parabola, we can get: C = - 3, ∵ y = x2 + bx-3, ∵ make an intersection point of the parabola and X axis between (1,0) and (3,0), ∵ substituting x = 1 into y = x2 + bx-3, we can get: y = 1 + B-3 < 0, substituting x = 3 into y = x2 + bx-3, we can get: y = 9 + 3b-3 > 0, ∵ - 2 < B < 2, that is, in the range of - 2 < B < 2

The shape of a parabola is the same as the image of y = - 1 / 3x ^ 2, the vertex is on the x-axis, and its symmetry axis is a straight line x = 2

Same shape
It can be:
y=-1/3(x-a)^2+b
The vertex is on the X axis, which means delta = 0
The axis of symmetry is x = 2, which means a = 2
If the analysis is like this, the result will not be sought

How to solve 3x-7 (x-1) = 12 - (x + 4)

3x - 7(x - 1) = 12 - (x + 4)
3x - 7x + 7 = 12 - x - 4
-4x + 7 = -x + 8
4x - x = 7 - 8
3x = -1
x = -1/3

Partition x ^ 3-2x ^ 2Y / x ^ 2y-2xy ^ 2

First, the numerator denominator is reduced to X (x ^ 2-2xy) / (xy-2y ^ 2)
In extracting the common factor X (x-2y) / Y (x-2y)
About X / Y