The function f (x) = LG [(kx-1) / (x-1)], k > 0

The function f (x) = LG [(kx-1) / (x-1)], k > 0

True number (kx-1) / (x-1) > 0
Because k > 0, (x - 1 / k) (x - 1) > 0
(1) When 1 / k = 1, that is, k = 1, (x-1) (x-1) > 0
The solution is x ≠ 1
(2) When 1 / k > 1, it means 0
It is known that the function f (x) = LG [(kx-1) / (x-1)], k > 0.
The domain of function should satisfy
1.(kx-1)/(x-1)>0
2.x≠1
Therefore, it can be considered in three situations:
When 01, 0.
The domain of function should satisfy
1.(kx-1)/(x-1)>0
2.x≠1
Therefore, it can be considered in three situations:
When 01,
1/k
What is the range of the function y = cos2x + 8cosx
y=cos2x+8cosx
= 2*(cosx)^2 - 1 + 8cosx
Let t = cosx
Then t ∈ [- 1,1]
t = 2t^2 + 8t -1
=2(t+2)^2 -10
The axis of symmetry is t = - 2
Opening up
Then when t = - 1, take the minimum value y = - 8;
When t = 1, the maximum value is 8
So the range is {Y-8
y=cos2x+8cosx=2cos²x-1+8cosx=2(cosx+2)²-5,-1
A point starts from a certain point on the number axis, first moves 5 unit lengths to the right, and then moves 2 unit lengths to the left. If the number represented by this point is 1, then the number represented by the starting point should be 1______ .
As shown in the figure: 1 move 2 units to the right, the length is 3, and then move 5 units to the left, the length is - 2
Examples of phrases used in English writing?
What phrases are used in English writing?
For academic, except for example, for instance, such as
Thank you for your help~
Case in point we out to follow their example another representative case the next example illustratethe other parallel case is given that
Given that the definition field of function f (x) = LG (KX ^ 2-kx + 1-k ^ 2) is (0,1), then the value range of real number K
kx^2-kx+1-k^2>0 0
The monotone increasing interval of function y = Log1 / 2 (- x ^ 2 + 4x + 12) is
Let t = - X & # 178; + 4x + 12
Y = Log & # 189; t, is a decreasing function
So the decreasing interval of T = - X & # 178; + 4x + 12 is the increasing interval of the original function
t = -x² +4x +12 = - (x-2)² +16
Minus interval (2, + ∞)
It is the increasing interval of the original function
can't
Let y = - x ^ 2 + 4x + 12 > 0, get - 2
After the point representing 1 on the number axis moves 2 length units, the corresponding number of the point is () or ()
-1 or 3
What are the summative phrases in English writing?
In a word, to include, finally, all in all, etc
If the domain of function f (x) = LG (KX ^ 2 + 4kx + 3) is r, then the value range of K is r
If the definition field of function f (x) = LG (KX ^ 2 + 4kx + 3) is r
Then KX & # 178; + 4kx + 3 > 0 holds
Let y = KX & # 178; + 4kx + 3 be a parabola and the axis of symmetry x = - 2
1.0
3. When k > 0, the opening of the image is upward
Only y min = f (- 2) = 4k-8k + 3 > 0
The solution is K
KX ^ 2 + 4kx + 3 > 0 is constant, that is, the discriminant of the root of the quadratic function is less than zero, k > 0 solves the inequality, or K = 0. Question: the discriminant of the root of a quadratic function is less than zero
Let f (x) = x2 + X + 12 be defined as {n, N + 1} (n is a natural number), then there are two functions in the range of F (x)______ This is an integer
When n ≥ 1, f (x) is monotonically increasing on [n, N + 1], f (n + 1) - f (n) = (n + 1) 2 + (n + 1) + 12-n2-n-12 = 2n + 2, so the number of integers in the range of F (x) is 2n + 2, when n = 0, the range of values is [f (0), f (1)] = [12, 52], and there are two integers 1 and 2