It is known that f (x) = ax + B / 1 + X2 is an odd function over (- 1,1), and f (1 / 2) = 2 / 5 (1) Finding the analytic expression of function f (x) (2) It is proved that f (x) is an increasing function on (- 1,1) by the definition of function monotonicity (3) Solving inequality f (t-1) + F (T)

It is known that f (x) = ax + B / 1 + X2 is an odd function over (- 1,1), and f (1 / 2) = 2 / 5 (1) Finding the analytic expression of function f (x) (2) It is proved that f (x) is an increasing function on (- 1,1) by the definition of function monotonicity (3) Solving inequality f (t-1) + F (T)

(1) F (x) = (AX + b) / (x ^ 2 + 1) is an odd function, f (- x) = - f (x) (- ax + b) / (x ^ 2 + 1) = - (AX + b) / (x ^ 2 + 1), - ax + B = - ax-b, B = - B, so B = 0. And f (1 / 2) = 2 / 5, so (A / 2) / (1 / 4 + 1) = 2 / 5, a = 1

It is known that the function f (x) whose domain is r satisfies f (x) + F (x + 2) = 2x-4x + 2, f (x + 1) - f (x-1) = 4 (X-2)
Problem (1) finding the analytic expression of F (x)
(2) If f (t-1), - 0.5, f (T) is an arithmetic sequence, find the value range of T
f(x+2)-f(x)=4x-4
How did you get here?
3Q！

1) By condition
f(x)+f(x+2)=2x^2-4x+2
f(x+2)-f(x)=4x-4
It can be concluded from the above two formulas
f(x)=x^2-4x+3
2) Because f (t-1), - 0.5, f (T) is an arithmetic sequence
So f (t-1) + F (T) = - 1
Substituting t = 2 or T = 3
^_ ^The prince of mathematics and chemistry is here!
Supplement:
By title
f(x+1)-f(x-1)=4(x-2)
Using X + 1 to replace x
f(x+1+1)-f(x+1-1)=4(x+1-2)
Namely
f(x+2)-f(x)=4x-4

Rational number of mathematical problems: mixed addition and subtraction, addition, subtraction, multiplication, division each 14 and answers

1+999-100=900 10+100-10=100 （-1）+（-2）-（-3）=0 50+52-3=99
（-1）-（-1）+（-2）=-2 20-9+11=22 10+11-20=1 5+5-1=9 8-1+2=9
（-10）-（-1）+2=-7 50+10-（-40）=100 10-20+5=-5 11+1-（-23）=-11 1+1-9=-7 1+9-12=-2
1+（-1）=0 999+11=1010 999+555=1554 111+121=232 111+（-122）=-11 9+1212=1221 88+22=110 77+11=88 555+212=767 25+333=358
444+323=767 333+222=555 2121+12=2133 110+120=230
1-（-1）=2 111-99=12 555-112=443 501-105=396 101-102=-1 555-99=454 767-676=91 887-778=109 991-882=99 101-121=-20 1-（-2）=3 122-112=10 132-123=9 442-424=18
1*（-1）=-1 20*15=300 50*（-2）=-100 555*11=6105 55*11=605 210*11=2310 11*11=121 75*11=825 99*11=1089 10*121=1210 12*11=132 33*11=363 22*11=242 111*11=1221
21&3=7 22&2=11 24&4=3 24$8=3 25&5=5 26&2=13 27&3=9 28*2=14 30&3=10 32&2=16 33&3=11 34&0=0 35&5=7 -36&（-3）=108

The position of a, B, C on the number axis is shown in the figure, and | a | = | C | (1) compare the size relationship of a, - A, B, - B, C, - C. (2) simplify | a + B | - | A-B | + | B + (- C) | + | a + C |

(1) Solution 1: according to the relationship between two points representing opposite numbers on the number axis, find out the corresponding points of - A, - B, - C, as shown in the figure. From the position relationship on the figure, we can see that - b > A = - C > - a = C > B. solution 2: from the figure, a > 0, B < 0, C < 0, and | a | = | C | = | B |, | - b > A = - C > - a = C > B. (...)

Ask a math problem: solve the equation AX + b-3x + 2Ab / 3 = 1 / 2 about X

The original equation can be said to be
(a-3)x+b+2ab/3=1/2
(a-3)x=1/2-b-2ab/3
x=(1/2-b-2ab/3)/(a-3)

The usage of quantities of
Large quantities of cotton ( ) shipped all over the world already.A large quantity of bamboo ( ) used for pipes to carry water.
A. has been,are B.has been,is C.have been,is
D.have been,are
Please tell me the usage

c
The following verbs are used with quantity
There are three arguments about the consistency between the subject and the predicate of "a quantity of" and "quantities of"
A. A quantity of / quantities of + n. + predicate, where the singular and plural forms of the predicate are consistent with the singular and plural forms of quantity
Quantities of nuts were on the table.
A quantity of nuts was on the table.
B. For a quantity of + n. + the singular and plural forms of the predicate are the same as those of a lot of, that is, they follow the principle of consistent meaning;
The predicate in the quantity of + n. + predicate must be plural
There is only a small quantity of wine left.
A large quantity of air conditions have been sold since the summer came.
Huge quantities of oil were shipped to Japan last year.
C. The singular and plural forms of the predicates in a quantity of / quantities of + n. + are the same as those in a lot of / lots of, that is, they follow the principle of consistency of meaning
Great quantities of sand was washed down the hillside by the rain last night.
All the teachers are arguing all the time. Generally speaking, it's just a simple and complex cooperation with quantity

If AB = 1, AC: bc4:1, then the length of CD is

BC ^ 2 + AC ^ 2 = AB ^ 2 = 1, so BC ^ 2 = 1 / 17, s (area) = 2 / 17,
CD=2S/AB=4/17

English phrases of class rules
For example, "no running in the hallway." and other English phrases are class rules

Don't eat in class.don 't run in the hall.don 't sleep in class.don 't talk when teacher is speaking.

WTO APEC ATM EMS UFO CEO SOS NBA full name in Chinese?
As much as you know, thank you!
It must be the full name of Chinese!

WTO World Trade Organization
APEC Asia Pacific Economic Cooperation
ATM automatic teller machine
EMS express mail service
UFO UFO
CEO Chief Executive Officer
SOS emergency signal
NBA National Basketball Association

the police came and they soon got the situation well------ a.by hand b.in hand c.on hang dwith hand

b. In hand
The police came and soon got hold of the situation