English translation Please translate these four words

English translation Please translate these four words

See personally or see in person or see by oneself
Personal point of view
Is that the four?
see by my/your/her/his/one's self
=Fixed collocation
1.She herself came to see me.=She came to see me herself.
She came to see me in person.
2.He came to see me personally.
No, he came to see me in person
How to say not only phrases in English
Not only:
1. not the only one
2. not only
3. not just
Examples and usage:
He is not only strong, but also smart
He is not only strong and healthy but also very smart.
Not only you but also I am to blame
Not only you but (also) I am to blame.
She is not only beautiful, but also kind
Not only is she beautiful, but she is (also) kind.
He is famous not only for his talent, but also for his kindness
He is famous not only for his talent but (also) for his kindness.
Jack is not only a good student, but also a basketball player
Jack is not only a good student but also a basketball player.
She can not only play, but also compose
She not only plays well, but also writes music
not only, but also
not only
Finding the range of logarithmic function~
The range of function y = log3 (1-2 ^ x-1) is
Logarithm requires the true number to be greater than zero
So 1-2 ^ X-1 > 0 and 2 ^ X-1 > 0, so only 2 ^ X-1 is needed
Now see these headache, ha ha, forget almost
A
Given the function f (x) = 2-x ^ 2, G (x) = X. if f (x) = min {f (x), G (x)} is defined, then the maximum value of F (x) is?
1、 Draw the image of F (x) and G (x) in a rectangular coordinate system, a straight line and a parabola (opening downward)
2、 Find out the intersection of two curves (the curve also includes straight line, I don't know what level of the building owner, forgive me), that is to solve the y = 2-x ^ 2 and y = x equations, the intersection is a (- 2, - 2), B (1,1)
3、 If we look at the case of two curves, between the intervals (- 2,1), f (x) > G (x), so f (x) is the smaller one, that is, f (x) = g (x) = x; similarly, on (- ∞, - 2] and [1, + ∞), f (x)
The maximum value of F (x) = 1
It's a new function made up of two images and the following curves.
Let f (x)
A topic about the period of function,
It is known that the function f (x) is an even function defined on R and satisfies f (x) = f (2-x). When x belongs to [0,1] f (x) = x ^ 2, if the equation f (x) - x-a = 0 has exactly two real solutions, then a=
A = 0, this kind of problem is a combination of number and shape. You can put the equation
The solution of the equation f (x) - x-a = 0 is regarded as the intersection of the straight line y = x + A and the curve y = f (x)
Because f (x) is an even function and if x belongs to [0,1] f (x) = x ^ 2, we can find the function image between [- 1,1]. Then we can know that the function period is 4 and in a period [- 1,5], the function image is symmetric with respect to x = 1 from F (x) = f (2-x)
It is found that when a = 2K (k = 0, + - 1, plus or minus 2,...), there are only two solutions, so this problem has a little defect. It is not that the two solutions are on [0,1]. A is the definite value, which is 0!
How to find the range of logarithm function,
 
When the true number can take all positive numbers, the range of logarithm function is r
In this problem, the true number of y = Log1 / 2 (x-1) is X-1. When x takes all real numbers greater than 1, X-1 takes all positive numbers,
Therefore, the value range is r, which can also be written as (- ∞, + ∞)
For real numbers C and D, we can use min {C, D} to represent the smaller number of C and D, such as min {3,} =. If y = min {,} of function X
For real numbers C and D, we can use min {C, D} to represent the smaller number of C and D, such as min {3, - 1} = - 1. If the image of the function y = min {2x square, a (x-t) square} about X is symmetric about the line x = 3, then the value of a and t may be
Let Y1 = 2x ^ 2, y2 = a (x-t) ^ 2, if y = min {Y1, Y2} may take part of Y1, then for x = 3 symmetry, Y2 is a part of y = 2 (X-6) ^ 2. When XY2, y = Y2 satisfies the meaning of the problem, a = 2, t = 6, if y = min {Y1, Y2} cannot take part of Y1
Is there any problem in the expression of the meaning of this question? Is the known condition related to the given function? It's urgent for explanation.
First, according to the function y = 2x2, the symmetry axis of the function is y-axis. Because the two functions are symmetrical about the straight line x = 3, the opening direction and size of the two functions are the same, so a = 2, so the symmetry axis of the function y = a (x-t) 2 is x = 2 × 3 = 6, so the value of t can be obtained,
The opening direction and size of the two functions are the same,
∴a=2，
The symmetry axis X = 2 × 3 = 6 of the function y = a (x-t) 2, i.e. t = 6... Expansion
First, according to the function y = 2x2, the symmetry axis of the function is y-axis. Because the two functions are symmetrical about the straight line x = 3, the opening direction and size of the two functions are the same, so a = 2, so the symmetry axis of the function y = a (x-t) 2 is x = 2 × 3 = 6, so the value of t can be obtained,
The opening direction and size of the two functions are the same,
∴a=2，
The axis of symmetry of the function y = a (x-t) 2 is x = 2 × 3 = 6, i.e. t = 6
Two questions about the period of function
1. The coordinates of all symmetry centers of the function y = 3sin (2x + π / 3) are_____ The equations for all the axes of symmetry are______ (specify)
2. Let f (x) be a function defined on the interval (- ∝, + ∝), for any x ∈ R, satisfy f (1-x) = f (x + 1) = f (x-3), and use IK to represent the interval [2k-1,2k + 1] (K ∈ z). When x ∈ IO is known, f (x) = x, find the expression of F (x) on the interval (- ∝, + ∝). (concrete process)
1. Let 2x + π / 3 = k π, then x = (3K-1) π / 6. The coordinate of the center of symmetry is ((3K-1) π / 6,0) and K is an integer
Let 2x + π / 3 = (2k + 1 / 2) π or (2k - 1 / 2) π, then x = (12K + 1) π / 12 or (12k-5) π / 12
The equation of symmetry axis is ((12K + 1) π / 12,1) or ((12k-5) π / 12, - 1) k is an integer
2. From F (1-x) = f (x + 1), we can see that f (x) takes x = 1 as the symmetry axis,
From F (x + 1) = f (x-3), f (x) = f (x + 4), that is, f (x) has a period of 4
If x ∈ IO = [- 1,1], f (x) = x, we can get f (x) = - x + 2 when x ∈ [1,3]
In other [- 1 + 4K, 3 + 4K] (k is an integer), the function image can be translated by the image on [- 1,3],
When x ∈ [- 1 + 4K, 1 + 4K], f (x) = x-4k
When x ∈ [1 + 4K, 3 + 4K], f (x) = - x + 2 + 4K
K is an integer
It's too hard~~~~
Calculation method of range of logarithmic function
Logarithmic function, that is, f (x) = loga (x), for its general form, when x is greater than zero, it is continuous, and the range of value is from negative infinity to positive infinity. If there is a composite part, we need to consider the value of the composite part. First, we calculate the value range of the composite part, and then use its continuity to calculate the value range of the total function
Let F X have f (x + y) = F X + F y for any real number xy and f x > 0
For any real number x, y, f (x + y) = f (x) + F (y)
Let x = y = 0, f (0) = 2F (0), f (0) = 0,
Let y = - x, then 0 = f (x) + F (- x),
F (x) is an odd function
Let x 10,
x> F (x) at 0