It is known that f (x) is a positive proportion function, G (x) is an inverse proportion function, and f (1) = 2g (1), f (2) + 4G (2) = 6. The expressions of F (x) and G (x) are determined

It is known that f (x) is a positive proportion function, G (x) is an inverse proportion function, and f (1) = 2g (1), f (2) + 4G (2) = 6. The expressions of F (x) and G (x) are determined

Let f (x) = KX, G (x) = A / X
k=2a
2k+4*a/2=6
The solution is as follows
k=2,a=1
f(x)=2x,g(x)=1/x
Given the function y = SiNx ^ 2 + sin2x + 3cosx ^ 2, find the minimum value of (1) function and the set at this time
(2) Monotone decreasing interval of function
(3) The image of this function can be obtained by how to transform the image of the function y = (2 under the root sign) sin2x
We need to be more detailed
Solution:
(1)
y=sinx^2+sin2x+3cosx^2=-1/2(-2sin^2x+1-1)+sin2x+3/2(2cos^2x-1+1)
=-1/2cos2x+1/2+sin2x+3/2cos2x+3/2
=cos2x+sin2x+2
=Root sign 2Sin (2x + π / 4) + 2
So the minimum is 2-radical 2
Then x = 5 π / 8 + K π
(2)
Y = radical 2Sin (2x + π / 4) + 2
So when
-π/2+2kπ
y=sinx^2+sin2x+3cosx^2=1+sin2x+2cosx^2
=1+sin2x+2cosx^2-1+1
=2+sin2x+cos2x
=2+sin（2x+π/4)
Now I will ask for No..... When sin (2x + π / 4) = - 1, the minimum value 2x + π / 4 = 2K π + 3 / 2 π x = k π + 5 / 4 π K ∈ Z is written as a set
2K... Unfold
y=sinx^2+sin2x+3cosx^2=1+sin2x+2cosx^2
=1+sin2x+2cosx^2-1+1
=2+sin2x+cos2x
=2+sin（2x+π/4)
Now I will ask for no answer..... When sin (2x + π / 4) = - 1, the minimum value 2x + π / 4 = 2K π + 3 / 2 π x = k π + 5 / 4 π K ∈ Z is written as a set
2kπ+1/2π＜2x+π/4＜2kπ+3/2π kπ+1/4π ＜x＜kπ+5/4π
Y = (2 under the root sign) sin2x shifts π / 8 to the left and then 2 units up
In the first question, I forgot to add the root 2 before sin (2x + π / 4)
It is known that the image of the first-order function y = KX + B and the image of the inverse scale function y = KX pass through the point a (- 2,3). The analytic expressions of the two functions are obtained
According to the meaning of the question, − 2K + B = 3K − 2 = 3, the solution is k = − 6B = − 9, so the analytic expressions of the two functions are y = - 6x-9 and y = - 6x
The square of SiNx of function 2 plus the minimum value of 1 divided by sin2x
X is between 0 and 90 degrees
Y = [2 (SiNx) ^ 2 + 1] / sin2x because (SiNx) ^ 2 = (1-cos2x) / 2, so y = (2-cos2x) / sin2x-y = (2-cos2x) / (0-sin2x) x at (0,90 °) 2x at (0180 °) can be regarded as the slope of the line from (0,2) point to (sin2x, cos2x), while (sin2x) ^ 2 + (cos2x) ^ 2 = 1 and 2x at
In the inverse scale function y = KX, the independent variable increases by 1 at x = 2, and the function value decreases by 23 correspondingly, then K=______ .
When x = 2, y = K2, because the independent variable increases by 1 at x = 2, the function value decreases by 23 correspondingly, that is, when x = 0.5, the function value is y + 1, and y-23 = K3, that is, k2-k3 = 23, and the solution is k = 4
Find the maximum and minimum of the square X of the function y = - 1-4sinx-cos
First, transform the function into the function with the same name, and use "1 = cos ^ 2x + sin ^ 2x" here
two hundred and twenty-two thousand three hundred and twenty-one
If the function value y of inverse proportional function y = K / X (k is not equal to 0) is at x = 1, the independent variable increases by 2, and the function value y decreases by 2 / 3, then k =?
It can be seen from the meaning of the title
k/（x+2）=y-2/3
Because when x equals 1, y = K
So y of the above formula is replaced by K, x + 2 = 1 + 2 = 3
k/3=k-2/3
K=1
Is f (x) = sin2x and G (x) = 2sinxcosx the same function? Is f (x) = cos2x and G (x) = cosx ^ 2-sinx ^ 2
What about f (x) 2cos ^ 2-1 and G (x) = 1-2sin ^ 2? And f (x) = tan2x and G (x) = 2tanx / (1-tanx ^ 2)?
How to judge?
All of them are the same set of functions. The formula sin (x + y) = sinxcosy + cosxsinycos (x + y) = cosxcosy sinxsiny, cosx ^ 2 + SiNx ^ 2 = 1 holds, so (1) sin (x + x) = sinxcosx + cosxsinx = 2sinxcosx (2) cos (x + x) = cosxcosx sinxsinx = cosx ^ 2-sinx ^ 2 (3) 2cos ^ 2-1 = 2 (1-sinx ^ 2
Both groups are the same function
Both are the same function
Given the inverse proportional function y = K / x, when the independent variable increases from 1 to 3, the value of Y decreases by 1, then the value of K decreases
K / 1-k / 3 = 1. In this case, k = 3 / 2
X increases y, which shows that it is a decreasing function
This kind of problem as long as uses the numerical value to carry in, solves the difference equation to be possible
k/1 - k/3 = 1
k = 3/2
Find the maximum and minimum of the function y = cos2x + SiNx (| x | ≤ π 4)
Let SiNx = t, then t ∈ [- 22, 22], so y = 1-sin2x + SiNx = - (T-12) 2 + 54, t ∈ [- 22, 22]. Therefore, when t = 12, that is, x = π 6, ymax = 54, when t = - 22, that is, x = - π 4, ymax = 1-22