If the image of a power function is known to pass through a point (8,1 / 2), then f (1 / 512)=

If the image of a power function is known to pass through a point (8,1 / 2), then f (1 / 512)=

The power function is f (x) = x ^ a
Over (8,0.5)
0.5=8^a
2^(-1)=2^3a
a=-1/3
f(x)=x^(-1/3)
f(1/512)=(1/512)^(-1/3)=[2^(-9)]^(-1/3)=2^3=8

If the image of power function J (x) passes through (4,2), then the value of F (1 / 8) is?

Let J (x) = x ^ A, bring in (4,2), get a = 1 / 2, J (x) = √ x, so f (x) = √ 2 / 4

On the inequality system of X {2x + a ≥ 4,5x-a

2x+a≥4
2x≥4-a
x≥(4-a)/2
5x-a

The image passing through the inverse scale function y = K / X (k is not equal to 0) of point (5,1) is as shown in the figure, which is calculated by using the image;
1. When x is greater than or equal to 1, the value range of Y; 2. When y ＞ - 2, the value range of X
As shown in the figure, the image of linear function Y1 = KX + B intersects with the image of inverse scale function y2 = m / X at two points a and B
1. Find the analytic expressions of inverse proportion function and linear function;
2. Using the function image, when x is what value, Y1 > Y2?

Analytical formula: y = 5 / X
（1）
Let x = 1, then:
y=5/1=5
Because when x > = 1, the function is monotone decreasing
X > 0, so Y > 0
So the value range of Y is 0

If the product of several rational numbers is negative, then the number of negative factors is zero______ ．

According to the multiplication rule of several non-zero rational numbers, when there are odd negative factors, the product is negative. For example: (- 1) × (- 2) × (- 3) × 4 = - 24, there are three negative factors, and the product is negative

6x-7=4x-5 x=?
6x-7 = 4x-5 find the value of X

We get 2x = 2, x = 1

The proper method is to solve the equation: (1): the square of X + 3x = 10 (2): (X-2) - 8 = 0 (3): (5x-3) - 2 (5x-3) - 3 = 0

(1) : the square of X + 3x = 10
x(x+3)=0
X = 0 or x = - 3
(2) The square of (X-2) - 8 = 0
（x-2)²=8
x-2=±2√2
X = 2 + 2 √ 2 or x = 2-2 √ 2
（3）：（5x-3）²-2（5x-3）-3=0
[(5x-3)-3][(5x-3)+1]=0
(5x-6)(5x-2)=0
X-6 / 5 or x = 2 / 5

Solving inequality 4x & # 178; + 4x + 1 > 0

Solution
4x²+4x+1>0
(2x+1)²>0
∵(2x+1)²≥0
∴2x+1≠0
∴x≠-1/2

How does the computer classify the calculation results
For example: a group of letters are a, B, C, D, e, F, G, h, I, J, K, l, m, y, x, T. If I want to divide a, C, h, I into "need" class, F, e, B, y, J into "don't need" class, and l, m, t, x into another class, how can I set the function by computer
For example: a group of letters are a, B, C, D, e, F, G, h, I, J, K, l, m, y, x, T. I want to divide a, C, h, I into "need" category, F, e, B, y, J into "don't need" category, and l, m, t, x into another category. How to set up function expression with computer

This is simple, as long as the character is required, the class will assign 1
No assignment of - 1 is required
Another is 0
Three judgments can be made using the selection loop

Mathematical problems of quadratic equation of one variable in grade three of junior high school
In golf competition, the relationship between the flight height h (m) of a mobilized ball in the air and the flight time t (s) is h = - t (T-7)
(1) After how many seconds, the height of the ball is 10m?
(2) How many seconds after scoring, the ball fell to the ground again

(1) After how many seconds, the height of the ball is 10m?
When h = 10, i.e. 10 = - t (T-7), the solution is t = 2 or T = 5
2) How many seconds after scoring, the ball fell to the ground again
When h = 0, i.e. 0 = - t (T-7), the solution is t = 0 (rounding off) or T = 7