On the symmetry of function image 1. If f (x) + F (A-X) = B, then the two images are symmetric with respect to (A / 2, B / 2) How to prove it? 2. Are there any relevant conclusions? 3. We know that f (x) + F (- x) = 3. Why can we find the value of F-1 (x-1) + F (4-x) and why it also applies to the first conclusion? F-1 (x-1) + F (4-x) is the inverse function of F-1 (x-1) + F-1 (4-x).

1. Prove that the symmetric point of point P (x, y) with respect to point Q (A / 2, B / 2) is p '(A-X, y-b). If point P (x, y) is on y = f (x), and y + F (A-X) = b, then B-Y = f (A-X), that is, point P' (A-X, y-b) is also on y = f (x), the function image is symmetric with respect to point Q (A / 2, B / 2). 2. This result is the definition of odd function "for function y = f (x)

Given the function y = X-2 (1) is it an odd function or even function (2) what kind of symmetry does its image have? (3) it is in (0,

(1) Non odd and non even functions
(2) It's a straight line. Where's the symmetry?!
(3) What's the problem?
The intersection axes of images are at (0, - 2) and (2,0)
The equation of the vertical line passing through the origin is y = - x, intersecting the original line at (1, - 1)

The image symmetry of the function y = sin (x + π / 3) is ()

On x = k π + π / 6 symmetry

1 / 8 plus (7 / 30 plus 1 / 8) multiply by 15

1 in 8 plus (7 in 30 plus 1 in 8) times 15
= 1 / 8 + 7 / 30 × 15 + 1 / 8 × 15
= 1 / 8 + 7 / 2 + 15 / 8
= (1 / 8 + 15 / 8) + 7 / 2
＝2＋3.5
＝5.5

The domain of definition of odd function y = f (x) is R. when x ≥ 0, f (x) = 2x-x & # 178;, if x ∈ [a, b], the domain of value of y = f (x) is [1 / B, 1 / a], the value of a, B is obtained

For Dashen, the process is simpler. In addition, I hope to increase the reward to 200 + 50
x<0,f(x)=2x+x²
From the known a & lt; B, we get 1 / B & lt; 1 / A
The same sign of a and B
(1) A, B are positive,
Then 1 / a ≤ 1
∴ a≥1
F (x) is a decreasing function on [a, b]
∴ f(a)=1/a,f(b)=1/b
That is, a and B are the roots of the equation 2x-x & # 178; = 1 / X
∴ x³-2x²+1=0
∴ (x-1)(x²-x-1)=0
X = 1 or x = (1 ± √ 5) / 2
∴ a=1,b=(1+√5)/2
(2) A, B are negative
Then 1 / b ≥ - 1
∴ b≤-1
Similarly, f (x) is a decreasing function on [a, b]
∴ f(a)=1/a,f(b)=1/b
That is, a and B are the roots of the equation 2x + X & # 178; = 1 / X
∴ x³+2x²-1=0
∴ (x+1)(x²+x-1)=0
X = - 1 or x = (- 1 ± √ 5) / 2
∴a=(-1-√5)/2,b=-1
To sum up, a = 1, B = (1 + √ 5) / 2 or a = (- 1 - √ 5) / 2, B = - 1

Overlap 5 pieces of square paper with side length of 10 cm as shown in the figure. What's the perimeter of this figure? What's the perimeter of 100 pieces of paper

Perimeter of five sheets = 5 × 10 × 4-4 × 5 × 4 = 120 (CM)
100 sheets of paper, its circumference = 100 × 10 × 4-99 × 5 × 4 = 2020 (CM)

How do the four operations of 3,3,8 and 8 equal to 24?

8/(3-8/3)=24

It is known that the sum of the first n terms of the sequence {an} is Sn, and an = Sn · sn-1 (n is greater than or equal to 2, Sn is not 0), A1 = 2 / 9
1. Proving {1 / Sn} as arithmetic sequence
2. Finding the set of natural number n satisfying an > an-1
Ask for detailed explanation, especially the second question,
Why 1 / Sn = 9 / 2 - (n-1) = (11-2n) / 2

An = SN-S (n-1) = Sn × s (n-1) 1 / S (n-1) - 1 / Sn = 11 / sn-1 / S (n-1) = - 1 {1 / Sn} is an arithmetic sequence with tolerance of - 1. When an = SN-S (n-1) = 1 / A1 = 9 / 21 / Sn = 1 / S1 + (n-1) d = 9 / 2 - (n-1) = (11-2n) / 2Sn = 2 / (11-2n) n > = 2, an = SN-S (n-1) = 2 / (11-2n) - 2 / (11-2 (n-1)) = 4 / ((11-2n) (1

It takes 125 bricks to pave the floor with 16 decimeters of square bricks. How many bricks do you need to pave the floor with one meter of square bricks? (Hello, please list the detailed process. If you are a teacher, please let me know,

The key to solve the problem is to keep the area of the land unchanged
Arithmetic:
1 meter = 10 decimeters
16×16×125÷（10×10）
=32000÷100
=320 (pieces)
1 meter = 10 decimeters
We need x bricks
10×10×x=16×16×125
100x=32000
x=320
A: 320 bricks are needed

Simple calculation 1.1 + 3 + 5 + 7 + 9 +... + 49 2. Half + three fourths + seven eighths plus fifteen sixteenth

1. This sequence is an arithmetic sequence
Sum = (first item + last item) × number of items △ 2
Number of items = (last item first item) △ tolerance + 1
Number of items = (49-1) △ 2 + 1 = 25
Sum = (1 + 49) × 25 △ 2=
2,1/2=1-1/2
3/4=1-1/4
7/8=1-1/8
15/16=1-1/16
So the original formula = 4 - (1 / 2 + 1 / 4 + 1 / 8 + 1 / 16)
=4-15/16
=3 and 1 / 16