If the power function y = f (x) is known to pass through a point (1 / 2,8), then f (- 3)

If the power function y = f (x) is known to pass through a point (1 / 2,8), then f (- 3)

Let the power function y = f (x) = x ^ a
Then the image of power function y = f (x) passes through the point (1 / 2,8)
That is, (1 / 2) ^ a = 8
That is, (2) ^ (- a) = 8
That is - a = 3
A = - 3
Then y = f (x) = x ^ (- 3)
So f (- 3) = (- 3) ^ (- 3)
=1/(-3)^3
=-1/27

If the image of power function is known to pass through point (8,1 ‖ 4), the value of F (27) can be obtained?

Given the power function of the image point (8,1 / 4), find the value of F (27)?
[solution] let the power function be y = x ^ α, and the point (8,1 / 4) be substituted into the result,
1 / 4 = 8 ^ α, i.e. 2 ^ (- 2) = 2 ^ (3 α),
3α=-2,α=-2/3.
Then y = f (x) = x ^ (- 2 / 3),
∴f(27)=27^ (-2/3)=3^(-2)=1/9.

Given the inequality system X - (5x-7) / 5 > 3 - (2x + 5), 1.5C - (x + 1) / 2 > (C-X) / 2 + (2x-1) / 2, it is to determine the value range of C, so that the inequality system satisfies the following conditions
Make the inequality system satisfy the following requirements: ① there is only one integer solution, ② there is no integer solution

x-(5x-7)/5>3-(2x+5),
5x-(5x-7)>15-5(2x+5),
7>15-10x-25,
10x>-17.
x>-1.7.
1.5c-(x+1)/2>(c-x)/2+(2x-1)/2,
3c-(x+1)>(c-x)+(2x-1),
3c-x-1>c+x-1,
2x

If the system of inequalities 2x + 3 ＞ 5x-6, the solution of X ＜ m + 2 is the range of M for X ＜ 3

2x+3＞5x-6 (1)
x＜m+2 (2)
3x from (1)

System of inequalities {3 (x + 2) + 5 (x-4)

Problem solving:
The solutions of the inequalities are as follows
x

At the same time, the product of all integers with inequality-3 (x + 1) > 2-5x and 1 / 2x-1 ≤ 7-3 / 2x is?

Solution - 3 (x + 1) > 2-5x
﹣3x－3＞2-5x
2x＞5
x＞5／2
1/2x-1≤7-3/2x
1／2x＋3／2x≦7＋1
2x≦8
x≦4
∴5／2＜x≦4
So this integer x is 3,4
So the product of all integers satisfying the condition is 3 × 4 = 12

Solving equation 8x △ 9 / 5 = 6 / 5

8x=6/5×9/5
8x=54/25
x=54/25÷8
x=27/100

Solve the equation. 8x + 3 × 0.9 = 6.3

8X+3×0.9=6.3
8x=6.3-2.7
8x=3.6
x=0.45

Solve the equation, X ＾ 2 + 8x-9 = 0

1 9
1 -1
1*(-1)+1*9=8
(x+9)(x-1)=0
x1=-9 x2=1

On line solution of equation 8x + 3x0.9 = 5.9

8x+3X0.9=5.9
8x+2.7=5.9
8x=5.9-2.7
8x=3.2
x=3.2/8
x=0.4