If the function f (x) = log2 (x2 ax + 3a) is an increasing function on [2, + ∞), then the value range of a is______ ．

If the function f (x) = log2 (x2 ax + 3a) is an increasing function on [2, + ∞), then the value range of a is______ ．

The function f (x) is monotone increasing function on [2, + ∞), so it should have A2 ≤ 222 − 2A + 3A > 0. The solution is - 4 < a ≤ 4, which is the value range of real number A. so the answer is - 4 < a ≤ 4,

Let the complete set be r, a = {x 3 less than or equal to x less than 7}, B = {x 2 less than x less than or equal to x less than 10}, find Cr (A and b), (CRA) intersection B

A={x|3

Let the complete set be r, set a = {x | a ≤ x ≤ a + 3}, CRB = {x | - 1 ≤ x ≤ 5}. (1) if a intersection B = empty set, find the value range of A. (2) if a intersection B = a, find a

1 ∩ a ∩ B = empty set
(1) a is less than a + 3 and less than - 1
② 5 is less than a and less than a + 3
① : A is less than a + 3 A + 3 is less than - 1
Solution: A is less than - 4
② : a up to 5, a + 3 up to - 1
Solution: A is equal to 5
To sum up, a is less than - 4 or a is greater than 5

If the function f (x) = loga (x ^ 2 + 8 - (9 / x)) is an increasing function in [1, + infinity], then the range of a
I want to solve the problem in detail

Let u (x) = x ^ 2 + 8, V (x) = 9 / x, draw the image of U (x) and V (x) in the same plane rectangular coordinate system, it is easy to see that the solution set of inequality U (x) - V (x) > 0 is (- ∞, 0) ∪ (1, + ∞), then the definition domain of function f (x) = loga (x ^ 2 + 8 - (9 / x)) is: (- ∞, 0) ∪ (1, + ∞)

If loga + logb = 0 (where a ≠ 0b ≠ 1), then f (x) = the image of logax and G (x) = logbx___ .
Option: a about X axis symmetry B about line y = x symmetry
C is symmetric about the Y axis and D is symmetric about the origin

A.
loga+logb=0.ab=1,a=1/b
f(x)=logaX=lnx/ln1/b=-lnx/lnb
g(x)=logbX=lnx/lnb
f(x)=-g(x)

The relationship between F (x) = loga (- x), f (x) = - logax and f (x) = logax

F (x) = loga (- x) and f (x) = logax are symmetric about the Y axis,
F (x) = - logax and f (x) = logax are symmetric about X axis

Given the function f (x) = Log1 / 2 (a ^ X-B ^ x) (a, B are constants) (1) when a > 0, b > 0, find the domain of F (x)
There is another condition: and a is not equal to B

a> B, the domain is (0, + ∞)
a

Given the function f (x) = loga (2-x) + loga (x + 2) (0 < a < 1), if the minimum value of function f (x) is - 2, find the value of A

In the function problem, we first consider the domain of definition, from 2-x 〉 0, x + 2 〉 0, - 2 ＜ x ＜ 2
If f (x) = loga (4-x Λ 2), 0 ＜ (4-x Λ 2) 4, there is a minimum value, which indicates that when 4-x Λ 2 = 4, the minimum value is taken (otherwise there is no minimum value), so 0 ＜ a ＜ 1, (if a ＞ 1, the function has no minimum value), and loga4 = - 2, so a = 0.5

Let f (x) = loga (1-A / x), where 0 < a < 1,
(1) It is proved that f (x) is simply reduced on (a, positive infinity)
(2) Solving inequality f (x) > 1

(1) When 0 ＜ a ＜ 1 x belongs to (a, positive infinity), a / X decreases with the increase of X, and 1-A / x increases. Because 0 ＜ a ＜ 1, LGA (x) decreases. Therefore, the definition field of loga (1-A / x) decreasing (2) function is 1-A / x > 01 > A / x, that is, when xax1f (x) = loga (1-A / x) 1x > A, f (x) = loga (1-A / x) decreasing, f (x) > 1 = f (A / (1-A)). Therefore, X

If u = R, a = {x | x ＞ = 3}, then CUA=

{x］x＜3}