English translation Take turns, talk about, the people in the picture,

English translation Take turns, talk about, the people in the picture,

Turns,Talk about,The figures in the picture
Phrase: on one side On one side How to say in English?
I hope I can write more,
while ex. He is listening to the music while having his dinner.at the same time ex. He is having his dinner, and at the same time, he is listening to the music.
while,and,by the way,at the same time
While, at the same time
English phrases, how to say in English
English phrases
What are the following periodic functions?
A、xcosx B、sinx2 C、sin1/x D、sin2x
Let's take D and do the figure below to see that the period of D is π
Is 2logax a logarithmic function after all? = logax2 = loga1 / 2x = log root ax! Isn't that it again-
Definition of logarithmic function: function of the form y = logax (a > 0 and a is not equal to 1)
So it's based on a logarithmic function, not a compound function
Let f (b) be a real number of any number, and f (1) = 1
Finding f (x) with F (a-b) = f (a) - B (2a-b + 1)
2. If the function f (x) (x belongs to (- 1,1)) satisfies 2F (x) - f (- x) = LG (x + 1), find f (x)
Mainly the second question
Let f (x) be a function defined on the set of real numbers R, satisfying f (0) = 1, and f (a-b) = f (a) - B (2a-b + 1) for any real number a, B
Analysis: ∵ f (x) is defined as R, satisfying f (0) = 1, and for any real number a, B, f (a-b) = f (a) - B (2a-b + 1)
Let a = b = X
∴f(a-a)=f(a)-a(2a-a+1)==>1=f(a)-2a^2+a^2-a==>f(a)=a^2+a+1
∴f(x)=x^2+x+1
2. If the function f (x) (x belongs to (- 1,1)) satisfies 2F (x) - f (- x) = LG (x + 1), find f (x)
Analysis: the function f (x) (x ∈ (- 1,1)) satisfies 2F (x) - f (- x) = LG (x + 1) (1)
Let x = - X
Then, 2f (- x) - f (x) = LG (1-x) (2)
(1) + (2) get f (x) + F (- x) = LG (1-x ^ 2) (3)
(1) If + (3), 3f (x) = LG [(1-x ^ 2) (x + 1)] = LG (1 + x-x ^ 2-x ^ 3)
∴f(x)=1/3lg(1+x-x^2-x^3)
2f(x)-f(-x)=lg(x+1)
Let x = - T
2f(-t)-f(t)=lg(1-t)
Namely
2f(-x)-f(x)=lg(1-x)
Eliminating f (- x) simultaneously with 2F (x) - f (- x) = LG (x + 1)
The solution is f (x) = [LG ((x + 1) ^ 2 (1-x))] / 3
f（2-x）=f(x)
What is the cycle?
About what symmetry,
This is not a periodic function! This is symmetry!
Let x = 1-x be replaced by F (2-x) = f (x)
Then f (1-x) = f (1 + x)
Therefore: this function is symmetric. The axis of symmetry is x = 1. The more common symmetric functions are quadratic functions
This is about x = 1 symmetry
If a periodic function can become f (x + m) = f (x), M is the period
Let x = 1-x be replaced by F (2-x) = f (x)
Then f (1-x) = f (1 + x)
This is not a periodic function!! This is symmetry!
Find the range of logarithm function,
If f (x) = 3 * {log2 ^ [4 * (x + 1)]} + 2, the base number is 2, and the true number is [4 (x + 1)], find the range,
The range of logarithm function is r
That is log2 ^ [4 * (x + 1)] ∈ R
Then 3 * log2 ^ [4 * (x + 1)] ∈ R
So the range is r
Put the real number forward
fx=3×[4*(x+1)]}log2+2
It is equivalent to a function of first degree
X is from negative infinity to positive infinity, so FX is from negative infinity to positive infinity
For any real number a, B, Max {a, B} = {a, a ≥ B, B, a is defined
The first problem is drawing. Because it's not easy to draw, I'll just say it
Let's draw the coordinate system first. G (x) is an even function about y axis symmetry, and f (x) is a function of degree passing through 1, 2 and 4 quadrants
There are two intersections of G (x) and f (x). They are (- 2,4) and (1,1)
H (x) = max {f (x), G (x)} means the larger segment between segments
The minimum value of H (x) = max {f (x), G (x)} is the smallest value in the larger segment of each segment
(1) Draw a picture to find the intersection
(2) (- 2, 1) (2, + infinity) increasing
Other minus
I want to ask a question about the period of function
It is known that f [x] is a periodic function with period 1, then on [0,1}, f [x] = x2. Find the expression of F [x] on [0,2]
On [0,1}, f [x] = x2
Then, on [1,2}, f [x] = (x-1) ^ 2
Expressions on f [x] and [0,2]=
F (x) = x ^ 2, X on [0,1}
F (x) = (x-1) ^ 2, X on [1,2}