Given the function g (x) = 1 + 2x, f [g (x)] = 1 + x2 / X2, find the expression of F (x)

Given the function g (x) = 1 + 2x, f [g (x)] = 1 + x2 / X2, find the expression of F (x)

f(1+2x)=(1+x^2)/x^2=1/x^2+1
Let t = 1 + 2x, then x = (t-1) / 2
Substituting into the above formula, f (T) = 4 / (t-1) ^ 2 + 1
So f (x) = 4 / (x-1) ^ 2 + 1

If the image of function f (x) is symmetric with respect to (- 1,2) and x = - 1, the expression of F (x) is obtained

f(x)=x^2+2x+3=(x+1)^2+2
It is not difficult to see that the vertex of this function is (- 1,2)
So when x > = - 1, f (x) = - (x + 1) ^ 2 + 2 = - x ^ 2-2x + 1
So f (x) = - x ^ 2-2x + 1 (x > = - 1)

Given the function f (x) = 2x + 1, X ∈ [1,5], try to find the expression of function f (2x-3)______ ．

∵ f (x) = 2x + 1, X ∈ [1,5], ∵ f (2x-3) = 2 (2x-3) + 1 = 4x-5, ∵ 1 ≤ 2x-3 ≤ 5, ∵ 2 ≤ x ≤ 4, so the answer is: F (2x-3) = 4x-5, X ∈ [2,4]

If f (x + 1 / x) = x / (1-x2), find the expression of function f (x)

t=1+1/x (1)
x=1/(t-1) (2)
F (T) = f (1 + 1 / x) = x / (1-x2) = f (x / (1 + x) (1-x)), if (2) is brought in, then f (T) = (t-1) / (t (T-2))
That is, f (x) = (x-1) / (x (X-2))

How to deduce the formula of the middle time velocity and the middle point velocity

1)
The velocity at half displacement is set to v
V^2-Vo^2=2a(S/2)
Vt^2-Vo^2=2aS
By comparison, v = root [(VT ^ 2 + VO ^ 2) / 2]
Let the velocity in the middle be v '
V'-Vo=a(t/2),
Vt-Vo=at
The two formulas are compared
V'=(Vo+Vt)/2

Practical problems of grade 6
1. In a 1:200 scale design drawing, the perimeter difference between the two squares is 4cm and the area difference is 25cm. The actual length of the sides of the two squares is () m and () m respectively
2. At present, the concentration of 10% brine is 20 kg. How many kg of 30% brine can be added to get 22% brine?
3. When a shop buys a batch of leather sandals, the selling price of each pair is 15% higher than the purchase price. If it sells all of them, it will make a profit of 120 yuan. If it only buys 80 pairs, the cost will be 64 yuan lower. How much is the purchase price of leather sandals?
4. Dongfang TV factory distributes a batch of parts to two workshops for processing. When the first workshop processes one third of the parts, there are still 84 parts left in the second workshop. When the first workshop processes the remaining tasks, the second workshop just completes two thirds of the tasks. How many parts are there in total?

1. Let the side length of the square be a ba-b = 1, the second power of A-B = 25a-b = 1 (a-b) (a + b) = 25 A-B = 1, a + B = 25 A = 13 B = 12. The actual side length of the two squares are 26m and 24m respectively. 2. Let x kg of 30% brine (2 + 0.3x) / (20 + x) =

It is deduced that the instantaneous velocity at the midpoint of the uniform velocity linear motion is equal to the average velocity during this period,

Initial velocity V1, final velocity V2, intermediate velocity V, total time t
Then v = V1 + at / 2
V2=V+at/2
By subtracting the two formulas, we get v = (V1 + V2) / 2

1. I can't figure out which fraction problems use multiplication and which use division
2. The meaning of score is not solid
3. The equation for sixth grade scores is not (1 + 1 / 7) X
4. The practical problems of comparison
Anyway, it's about fractional division and multiplication_

To find the fraction of a number by multiplication, to find the fraction of a number by division
Let me tell you a few more formulas
A more than B A-B / b b less than A-B / A
Equations are like integral equations

What is the difference between vulcanized rubber and NBR? Which is better?

Usually rubber can not be used directly, there is no cross-linking, elastic tensile strength is not good, after curing agent curing, that is vulcanized rubber, can be used to produce related products
NBR is produced by acrylonitrile and butadiene, with the characteristics of oil resistance and low temperature resistance
Different uses, can not reflect the good

Grade six of the four points application!
1. One wire uses 2 / 5 of it for the first time, and the remaining 3 / 10 for the second time, leaving 21 meters of wire. How long is this wire?
2. Xiao Li read a book. On the first day, she read 1 / 8 of the whole book and 16 more pages. On the second day, she read 1 / 6 of the whole book and on the third day, she read the remaining 86 pages. How many pages are there in this book?
3. Xiao Li read 49 pages of a book on the first day and 2 pages more than 1 / 8 of the whole book on the second day. The books she read in these two days are exactly half of the book. How many pages are there in total?
4. To build a highway, it takes 15 days for team a to build it alone, 20 days for team B to build it alone, and 3 days for the two teams to build it together. How many parts of the highway have been completed?
Big brother and big sister help! As long as complete, I swear I will chase points!
It's due tomorrow!

1. The first time you use 2 / 5 of a wire, the second time you use the remaining 3 / 10, the remaining 21 meters of wire. How long is the wire? The first time you use 2 / 5, the remaining 1-2 / 5 = 3 / 5, the second time you use 3 / 5 × 3 / 10 = 9 / 50, the remaining 3 / 5 × (1-3 / 10) = 21 / 50, the original length of the wire = 21 / (21 / 50) = 50 meters