Let the intersection of the image of the function y = x ^ 3 and y = 2 ^ (2-x) be (x0, Y0), then what is the interval of x0

The image of Y1 = x ^ 3 is in the first quadrant and the third quadrant, and is an increasing function,
The image of y2 = 2 ^ (2-x) is in the second quadrant and the first quadrant, and is a decreasing function
So the intersection must be in the first quadrant
When x = 1, Y1 = 1, y2 = 2
When x = 2, Y1 = 8, y2 = 1
So x0 must be in the interval (1,2)

Definition: if the function y = f (x) exists x0 (a < x0 < b) in a given interval [a, b] in the domain of definition, satisfying f (x0) = f (b) − f (a) B − a, then the function y = f (x) is called the "mean function" on [a, b], and x0 is its mean point. For example, y = X4 is the mean function on [- 1, 1], and 0 is its mean point. (1) judge whether the function f (x) = - x2 + 4x is on the interval [0, 9] Is it an average function? If so, find out its mean value; if not, explain the reason; (2) if the function f (x) = - x2 + MX + 1 is the mean value function on the interval [- 1,1], try to determine the value range of real number M

(1) From the definition, when the equation - x2 + 4x = f (9) − f (0) 9 − 0 of X has a real root in (0, 9), the function f (x) = - x2 + 4x is an average function in the interval [0, 9]. By solving - X2 + 4x = f (9) − f (0) 9 − 0 {x2-4x-5 = 0, we can get x = 5, x = - 1

For the function f (x), the domain of definition is d. if there exists x0 ∈ d such that f (x0) = x0, then (x0, x0) is called the fixed point on the image of F (x). & nbsp; therefore, the coordinates of the fixed point on the image of the function f (x) = 9x − 5x + 3 are______ ．

According to the definition of fixed point, we know that 9x − 5x + 3 = x has the solution of x = 5 or 1, so the fixed point on the function image has (1,1), (5,5), so the answer is (1,1) (5,5)

Definition: if f (x) has f (x0) = x0 for a certain number x0 in its domain, then x0 is said to be a fixed point of F (x)
Let f (x) = 3x ^ 2 + X + A, G (x) = 2aX + 1
(1) If f (x) has no fixed point on (0,2), the value range of a is obtained
(2) If X-1 ＜ f (x) - G (x) ＜ x + 1 holds for any x ∈ (0,1), the value range of a is obtained

Definition: if f (x) has f (x0) = x0 for a certain number x0 in its domain, then x0 is said to be a fixed point of F (x)
In fact, f (x) and the line y = x have intersections (x0, x0)
(1) If f (x) has no fixed point on (0,2), that is, there is no intersection between F (x) and y = x on (0,2)
That is, 3x ^ 2 + X + a = x has no root at (0,2)
3x^2+a=0
Let H (x) = 3x ^ 2 + a have no intersection at (0,2) and X axis
According to the image of quadratic function
H (0) ≥ 0 or H (2) ≤ 0, a ≥ 0 or 12 + a ≤ 0
So a ≥ 0 or a ≤ - 12
(2)f(x)-g(x)=3x^2+(1-2a)x+a-1
X-1 ＜ f (x) - G (x), that is, 3x ^ 2-2ax + a ≥ 0, is constant at (0,1)
Let K (x) = 3x ^ 2-2ax + A, then K (0) ≥ 0 and K (1) ≥ 0
Then 0 ≤ a ≤ 3
F (x) - G (x) ＜ x + 1, that is, 3x ^ 2-2ax + A-2 ＜ 0 holds in (0,1)
Let m (x) = 3x ^ 2-2ax + A-2, then K (0) ≤ 0 and K (1) ≤ 0
A ≤ 2 and a ≥ 1, i.e. 1 ≤ a ≤ 2
Intersection of 0 ≤ a ≤ 3 and 1 ≤ a ≤ 2
We get 1 ≤ a ≤ 2

The two right sides of a right triangle are 9cm and 6cm respectively. If you reduce them to 3cm and 2cm respectively, the hypotenuse will be reduced to one third of the original

It is known that the length of the right side of an isosceles right triangle is 1 meter, and the third side can be found
As the title, already know two sides are 1 meter right triangle. Find his hypotenuse length
It is stated here that the formula and specific numerical results should be given, because I feel that the formula is different from the actual number

The answer is root 2
In terms of formula, two right triangles with side length of 1m are isosceles right triangles, and the ratio of each side is 1:1: radical 2. The verification request is helpful to Pythagorean theorem~
Root 2 is very difficult to measure, measure out can be almost, after all, there are errors~

Given the length of two sides of a right triangle, how to calculate the angle

Party A + Party B = Party C
Sin angle = opposite / bevel

Given the length of two sides of a right triangle, how to calculate the length of the other side

Using Pythagorean theorem: the sum of the squares of the two right sides of a right triangle equals the square of the hypotenuse

(1) If the lengths of the two right sides of a right triangle are known to be 5 and 7, the length of the hypotenuse can be calculated; (2) if the lengths of the two sides of a right triangle are known to be 5 and 7, the length of the hypotenuse can be calculated
Find the length of the third side

If the lengths of the two right sides of a right triangle are 3 and 5, what is the length of the oblique side (Pythagorean theorem)

Oblique side length ^ 2 = 3 ^ 2 + 5 ^ 2 = 34
Oblique side length = √ 34

Let the intersection of the image of the function y = x ^ 3 and y = 2 ^ (2-x) be (x0, Y0), then what is the interval of x0