Make an image of y = x? - 2|x | - 3, and write the monotone interval of the function

Make an image of y = x? - 2|x | - 3, and write the monotone interval of the function

Because it is / X /, so x < 0 is symmetric with x > 0. If y = (/ X / - 1) ^ 2-4 knows that the parabola vertex is x = 1, then monotone interval is obtained

Given the function f (x) = x 2 – 2x, X ∈ [2,4], find the monotone interval and the maximum value of F (x) and draw the image It is best to find out the intersection point with X axis, the intersection point with y axis, the symmetry axis and the maximum value

f(x)=x^2-2x=(x-1)^2-1
Axis of symmetry of vertex (1, - 1) x = 1
Intersection with X axis (2,0) (0,0)
Intersection with y axis (0,0)
When drawing an image, pay attention to X ∈ [2,4]
f(x)min=0
f(x)max=8

Given y = log 4 (2x + 3-x? 2), find the function definition domain and monotone interval

(1) If y = log4 (2x + 3-x2) is meaningful, then 2x + 3-x2 > 0 is required, i.e. - 1 < x < 3
Therefore, the domain of y = log4 (2x + 3-x2) is (- 1,3)
(2) ∵ y = log4u, u = 2x + 3-x2, and y = log4u is an increasing function, so find the subtraction interval of the function value of u = 2x + 3-x2 greater than 0
∵u=2x+3-x2=-（x-1）2+4,
The minus interval of y = log4 (2x + 3-x2) is (1,3)

The known function f (x) = a − x The image symmetry center of the inverse function F-1 (x) of X − a − 1 is (- 1,3) 2) Then the monotone increasing interval of the function H (x) = loga (x2-2x) is () A. （1，+∞） B. （-∞，1） C. （-∞，0） D. （2，+∞）

Because the image symmetry center of the inverse function F-1 (x) of F (x) = a − XX − a − 1 is (- 1, 32), f (x) is symmetric about (32, − 1), because f (x) = − 1 − 1x − a − 1, so a + 1 = 32, so a = 12, so the definition domain of H (x) = loga (x2-2x) = log12 (x2 − 2x) H (x) is {x | x > 2 or X

The monotone decreasing interval of the function f (x) = log half [2 (- x 2 + 2x-1) + 1] is_______ . Hurry!

f(x)=log½[2(-x²+2x-1)+1]=log½[-2(x-1)²+1]
The logarithm is significant, and the true number is > 0
-2(x-1)²+1>0
2(x-1)²

Given the function f (x) = (log with a as the base B) x 2 + 2 (log with B as the base a) x + 8 is above the x-axis, find the value range of a and B

Log (B, a) denotes the logarithm of B based on a
Similarly, log (a, b) denotes the logarithm of a base B
If f (x) is above the x-axis, then
Log (B, a) > 0 leads to b > a
[2log (a, b)] ^ 2 - 4 log (B, a) * 8 < 0 let log (a, b) = t
So there are 4 T ^ 2 - 32 / T

It is proved that the function f (x) = x 2 + 6x is an increasing function on the interval [- 3, ∞]

Set - 3

It is proved that the function f (x) = x 2 is a decreasing function on the interval (negative infinity, 0)

It is proved that if x 1 ＜ x 2 ＜ 0, f (x2) - f (x1) = x2? - X1? = (x2-x1) (x2 + x1) < 0
Therefore, the function f (x) = x 2 is a minus function on the interval (- ∞, 0)

The monotone interval of the function f (x) = x? - x + 1 is pointed out

If x < 1 / 2, f '(x) < 0; if x > 1 / 2, f' (x) > 0, then the monotone increasing interval is (1 / 2, positive infinity), and the monotone decreasing interval is (negative infinite, 1 / 2)

The monotone interval of the function y = x + 1 / X is given. In the proof of monotonicity on the correlation interval, how does y = x + 1 / X become y '= 1-1 / x?

This is the derivative method,
See if the derivative is positive or negative,
Then the corresponding interval function is increased,
If it is negative, the corresponding interval function is minus