Y=k/x
A (-16; 2)
2=k/(-16)
k=2*(-16)= -32
y= -32/x
При x= -30
y= -32/(-30)= 16/15 = 1 ¹/₁₅
F(x) = -2cos(2x-П) + с
M(П/2;3)
3 = -2cos(2*П/2-П) + c
3 = -2cos0 + c
c = 3+2cos0 = 5
F(x) = -2cos(2x-П) + 5
![2^{ \frac{3}{x} } \geq 0,5 ^{x-4}](https://tex.z-dn.net/?f=+2%5E%7B+%5Cfrac%7B3%7D%7Bx%7D+%7D++%5Cgeq+0%2C5+%5E%7Bx-4%7D+)
![0,5^{x-4}=( \frac{5}{10} ) ^{x-4} = ( \frac{1}{2} )^{x-4}= (2^{-1} )^{x-4}= 2^{-1*(x-4)} = 2^{-x+4}](https://tex.z-dn.net/?f=+0%2C5%5E%7Bx-4%7D%3D%28+%5Cfrac%7B5%7D%7B10%7D+%29++%5E%7Bx-4%7D+%3D+%28+%5Cfrac%7B1%7D%7B2%7D+%29%5E%7Bx-4%7D%3D+%282%5E%7B-1%7D+%29%5E%7Bx-4%7D%3D+2%5E%7B-1%2A%28x-4%29%7D+++%3D+2%5E%7B-x%2B4%7D+)
![2^{ \frac{3}{x} } \geq 2^{-x+4}](https://tex.z-dn.net/?f=+2%5E%7B+%5Cfrac%7B3%7D%7Bx%7D+%7D++%5Cgeq++2%5E%7B-x%2B4%7D+)
основание степени а=2, 2>1. знак неравенства не меняем
![\frac{3}{x} \geq -x+4](https://tex.z-dn.net/?f=+%5Cfrac%7B3%7D%7Bx%7D++%5Cgeq+-x%2B4)
![\frac{3}{x}-(-x+4) \geq 0](https://tex.z-dn.net/?f=+%5Cfrac%7B3%7D%7Bx%7D-%28-x%2B4%29+%5Cgeq+0+)
![\frac{3+ x^{2}-4x }{x} \geq 0](https://tex.z-dn.net/?f=+%5Cfrac%7B3%2B+x%5E%7B2%7D-4x+%7D%7Bx%7D++%5Cgeq+0)
метод интервалов:
![1. \left \{ {{ x^{2} -4x+3=0} \atop {x \neq 0}} \right. , \left \{ {{(x-3)*(x-1)=0} \atop {x \neq 0}} \right.](https://tex.z-dn.net/?f=1.+%5Cleft+%5C%7B+%7B%7B+x%5E%7B2%7D+-4x%2B3%3D0%7D+%5Catop+%7Bx+%5Cneq+0%7D%7D+%5Cright.+%2C+++++%5Cleft+%5C%7B+%7B%7B%28x-3%29%2A%28x-1%29%3D0%7D+%5Catop+%7Bx+%5Cneq+0%7D%7D+%5Cright.+)
2. x₁=1,x₂=3, x≠0
- + - +
------[1]--------(0)-------[3]------------->x
3.
x∈[1;0)∪[3;∞)
Y / y - 9 - 9/ y - 9 = (y - 9) / ( y - 9) = 1
4x^2-1=0
4x^2=1 делим на 4
x^2=1/2 корень
x1=1/2
x2=-1/2