The monotone increasing interval of function FX = 1 / (X & # 178; + 2x + 2) is?

The monotone increasing interval of function FX = 1 / (X & # 178; + 2x + 2) is?

Let u = x ^ 2 + 2x + 2 = (x + 1) ^ 2 + 1
Then the original function becomes y = 1 / u
Let u be a decreasing function at (negative infinity, - 1]
And y = 1 / u is an increasing function
So the monotone increasing interval of function FX = 1 / (X & # 178; + 2x + 2) is
(negative infinity, - 1]

Find the decreasing interval of function y = LG [(1 / 2) ^ 2x-5 (1 / 2) ^ x + 6]

Change the element, t = (1 / 2) 2x, t decreases monotonically, then find the increasing interval of Y (T) by the method of derivative, finally find the interval of X according to t

The decreasing interval of function f (x) = LG (3-2x-x ^ 2) is

1. Satisfy 3-2x-x ^ 2 > 0 and F = 3-2x-x ^ 2 as monotone decreasing interval
The result is [- 1,1]

Find the monotone decreasing interval of function FX = | x + 1 | - | 2X-4 |

f(x)=|x＋1|－|2x－4|
First find out the endpoint values - 1, 2
Then we discuss it by category
① When x ≤ - 1
f(x)=－(x＋1)－[－(2x－4)]
=－x－1＋2x－4
=x－5
Is an increasing function
② When - 1

How does the inverse scale function y = - 1 / X change to 1-1 / x + 1
Please tell me the law of the change of the inverse proportion function, that is, what is added and subtracted, how is left added and right subtracted changed. Where is the add? Where is the right subtracted

Function transformation: the general method is to add left and subtract right directly after the function analytic formula along the Y axis
The x-axis is also left plus right minus
For the example you proposed, it should be like this: 1 unit up, 1 unit right

For the inverse scale function y = 2 / x, the following statement is incorrect ()
A. (- 2, - 1) on its image B. its image is in the first three quadrants C. when x > 0, y increases with the increase of X D. when x < 0, y decreases with the increase of X

C & nbsp; is wrong

For the inverse scale function y = k2x (K ≠ 0), the following statement is wrong ()
A. Its image is distributed in the first and third quadrants. B. y decreases with the increase of X. C. its image is centrosymmetric. D. points (k, K) are on its image

A. ∵ K ≠ 0, ∵ K2 ＞ 0, ∵ its image is distributed in the first and third quadrants, so this option is correct; B, ∵ its image is distributed in the first and third quadrants, ∵ in each quadrant, y decreases with the increase of X, so this option is wrong; C, ∵ this function is an inverse scale function, ∵ its image is a centrosymmetric graph, so this option is correct; D, ∵ K · k = K2, ∵ point (k, K) is in the first and third quadrants Its image, so this option is correct. So select B

For the inverse scale function y = k ＾ 2 / X (k is not equal to 0), the following statement is incorrect
1. Its image is distributed in one or three quadrants. 2. Points (k, K) are on its image. 3. Its image is centrosymmetric. 4. Y increases with the increase of X

Because K ^ 2 > 0
So in the first and third quadrants, y decreases with the increase of X
So choose D

For the inverse scale function y = 7 / x, it is incorrect to say that () a image must pass (1,7) b y and decrease with the increase of X
When D x > 1 in the first and third quadrant, y

It is not true that () b y decreases with the increase of X

Let F X satisfy f x = - f (x + 3 / 2) and f (1) = 1, then f (2014)=

f(x)=-f(x+3/2)
So f [(x + 3 / 2) + 3 / 2] = - f (x + 3 / 2) = f (x)
That is, f (x + 3) = f (x), f (x) is a periodic function of T = 3
So f (2010) = f (0) = 1