It is known that the function f (x) defined on (0, positive infinity) belongs to (0, positive infinity) for any x, y, and f (XY) = f (x) + F (y), And when 0 < x < 1, f (x) > 0, judge the monotone interval of F (x) on (0, positive infinity)

When X1 > x2 > 0, 0 < x2 / X1 0
f(x2)
= f(x1 * x2/x1)
= f(x1) + f(x2/x1)
> f(x1)
Therefore, f is a decreasing function over the whole domain

Given the function f (x) > 0, and f (XY) = f (x) * f (y), if x > 1, then f (x) > 1. Finding f (1) proves that f (x) increases monotonically on x > 0

1. F (1) = f (1 × 1) = f (1) × f (1), so f (1) = 0 or F (1) = 1, and f (x) > 0, so f (1) = 1
2. Let x 2 > x 1 > 0, then x 2 / x 1 > 1, and f (x 2 / x 1) > 1
F (x 2) = f (x 1 × x 2 / x 1) = f (x 1) × f (x 2 / x 1) > F (x 1) × 1 = f (x 1), that is, f (x 1) increases strictly monotonically on x > 0

|X+i|

【1】
Here, X is a real number. You didn't explain it clearly
【2】
X + I denotes an imaginary number, and | x + I | denotes the module of the imaginary number
Namely | x + I | = √ (X & # 178; + 1)
From the question set | x + I | 2, it can be concluded that:
(X & # 178; + 1) ＜ 2
x²+1＜2
The solution is X & # 178; < 1
∴-1＜x＜1

Given the square x + 2sinxcosx + 1 of the function f (x) = 2cos, ① find the minimum positive period of the function, ② find the monotone increasing interval of the function

Using the formula of double angle, the following results are obtained
F (x) = cos2x + sin2x + 2 = radical 2Sin (2x + pi / 4) + 2
So, the minimum positive period is pi,
The monotone increasing interval is: - pi / 2 + 2kpi

2（x-2.

x-2.6=4
x=4+2.6
The solution is x = 6.6

It is known that the center of the ellipse is at the origin, its left focus F1 coincides with the focus of the parabola y square = - 4x, M is an intersection of the ellipse and the parabola, and the absolute value of f1m = 3 √ 2-3
(1) The equation of finding ellipse

x²/2+y²=1

X-360 = 60 to solve the equation

360+60=15x
420=15x
x=28

What is (1 + cos X / 2) / 2 equal to?
Is it equal to half? How to calculate?

=1/2+cosX

Equation of circle (8 9:52:50)
Given that the distance from the moving point P to the fixed point a (8,0) is equal to twice the distance from P to the fixed point B (2,0), the trajectory equation of the moving point P is obtained

Let P (x, y),
According to the meaning of the title: [(X-8) ^ 2 + y ^ 2] ^ 1 / 2 = 2 [(X-2) ^ 2 + y ^ 2] ^ 1 / 2
(x-8)^2+y^2=4(x-2)^2+4y^2 ,
It is reduced to x ^ 2 + y ^ 2 = 16
It is the trajectory equation of point P,
It is a circle with the origin as the center and radius of 4

() / () = 9 / () = () / () put the eight integers 1-8 in the following brackets to make the equation hold
As soon as possible, please. I have an urgent need
It can't be repeated

(3)/(6)=9/(18)=(27)/(54)

It is known that the function f (x) defined on (0, positive infinity) belongs to (0, positive infinity) for any x, y, and f (XY) = f (x) + F (y), And when 0 < x < 1, f (x) > 0, judge the monotone interval of F (x) on (0, positive infinity)