It is known that f (x) is an odd function of the domain of definition in the interval (- 1,1). When x belongs to (0,1), f (x) = 2x / 4x + 1, the analytic expression of F (x) is obtained

It is known that f (x) is an odd function of the domain of definition in the interval (- 1,1). When x belongs to (0,1), f (x) = 2x / 4x + 1, the analytic expression of F (x) is obtained

F (x) is an odd function of the domain in the interval (- 1,1)
When x belongs to (0,1), f (x) = 2 ^ X / (4 ^ x + 1)
When x belongs to (- 1,0), - x belongs to (0,1),
f(-x)=2^(-x)/[4^(-x)+1]=-f(x)
f(x)=-2^(-x)/[4^(-x)+1]
x=0,f（x)=0
Therefore, the analytic expression of F (x) is as follows:
F (x) = {2 ^ X / (4 ^ x + 1), X belongs to (0,1)
{0,x=0
{- 2 ^ (- x) / [4 ^ (- x) + 1], X belongs to (- 1,0)

It is known that f (x) is an odd function defined on [- 1,1], and f (1) = 1. If a, B ∈ [- 1,1], a + B ≠ 0, f (a) + F (b) a + b > 0. Judge whether f (x) is an increasing or decreasing function on [- 1,1], and prove your conclusion

Let x1, X2 ∈ [- 1, 1], and x1 ＜ X2, then - x2 ∈ [- 1, 1]. And f (x) is an odd function, then f (x1) - f (x2) = f (x1) + F (- x2) = f (x1) + F (− x2) X1 + (− x2) · (x1-x2)

There is a pile of yellow sand on the construction site. One fourth of the total amount was used on the first day, and one fourth more than the first day on the second day. At this time, there are still 15 tons left. How many tons of yellow sand are there in total

15 / (1-1 / 4-1 / 4 * (1 + 1 / 4)) = 240 / 7 (ton)
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The known line y = 2x + 1 (1) and the known line about X-axis symmetry

It is known that (0,1) (1,3) is a point on a straight line, and the symmetric points of these two points about the X axis are (0, - 1) (1, - 3), so the symmetric line is y=
-2x-1.

If the ratio of male to female workers in a factory is 7:8, then the number of male workers is equal to that of female workers (& nbsp; & nbsp; & nbsp;); & nbsp; the number of female workers accounts for & nbsp; & nbsp; & nbsp; & nbsp;) of the total number of workers in the factory

A: then the number of male workers is equal to 78 of female workers; female workers account for 815 of the total number of workers in the factory

The factorization of (2Z & sup2; - 2x & sup2; - 2Y & sup2;) & sup2; - 16x & sup2; Y & sup2

The original formula = (2Z & sup2; - 2x & sup2; - 2Y & sup2; + 4xy) (2Z & sup2; - 2x & sup2; - 2Y & sup2; - 4xy)
=4[z²-(x²-2xy+y²)][z²-(x²+2xy+y²)]
=4[z²-(x-y)²][z²-(x+y)²]
=4(z+x-y)(z-x+y)(z-x-y)(z+x+y)

There are 20 boys in the school chorus, accounting for two fifths of the total number of the chorus. How many people are there in the chorus? How many girls are there?

Solution: the total number of students is X. 2 out of 5 x = 20 x = 20 * 5 out of 2 x = 50 answer: the total number of students is 50. 50-20 = 30 answer: there are 30 girls

First simplify the evaluation (x + 3 / x2-9) + (3 / x-3) where x = - 1

The original formula = (x + 3) / [(x-3) (x + 3)] + 3 / (x-3) = 1 / (x-3) + 3 / (x-3) = 4 / (x-3) substituting = - 1

There are four more girls than two-thirds of the boys in a class. If there are three fewer boys and four more girls, then the number of men and women is just the same. How many men and women are there in this class
Don't do it with equations

There are x boys and 2 / 3x + 4 girls in this class
X-3=2／3X+4+4
To solve this equation,
X=33
Female: 2 / 3x + 4 = 26
A: there were 33 boys and 26 girls in this class

5x-y=3,0.2x+0.3y=-0.9

5x-y=3,
0.2x+0.3y=-0.9
y=5x-3
0.2x+0.3(5x-3)=-0.9
0.2x+1.5x-0.9=-0.9
1.7x=0
x=0
y=5*0-3=-3
x=0
y=-3