Given that the function f (x) = log2 (x + 1) + alg2 (1-x) is an odd function, find the value of a and the analytic expression of F (x) It is known that the function f (x) = log2 ˇ (1 + x) + log2 ˇ (1-x) is an odd function. Find the value of a and the analytic expression of F (x)

Given that the function f (x) = log2 (x + 1) + alg2 (1-x) is an odd function, find the value of a and the analytic expression of F (x) It is known that the function f (x) = log2 ˇ (1 + x) + log2 ˇ (1-x) is an odd function. Find the value of a and the analytic expression of F (x)

f（-x）=log2 1-x+alog1+x=-f（x）=-log 2 1+x -alog2 1-x
Log21-x + Log1 + x = - log 21 + X - log21-x, so a / 1-x = 1-x is OK
If the minimum positive period of the function f (x) = sinax + cosax (a > 0) is 1, then a symmetry center of its image is ()
A. (−π8，0)B. （0，0）C. (−18，0)D. (18，0)
If f (x) = sinax + cosax = 2Sin (AX + π 4) t = 2 π a = 1, then a = 2 π, so f (x) = 2Sin (2 π x + π 4) Let f (x) = 0, then there is 2 π x + π 4 = 0x = - 18, that is, one of the symmetry centers is (- 18, 0), so C is chosen
The number corresponding to point a on the number axis is - 1. An ant starts from point a and climbs to the right along the number axis at the speed of 3 units of length per second to point B, and eats up point B in 2 seconds
Food, and along the original road at the same speed back to point a, share to 6 seconds, then the ant crawling distance is several unit length? B point and a point distance is how many unit length? B point corresponding number is how many?
The crawl time is 6-2 = 4 seconds
So the distance is 4 × 3 = 12 unit length
The AB distance is 12 △ 2 = 6 unit lengths
Rightward
So B is - 1 + 6 = 5
Making tea
As you pass by, my elder brother and elder sister are in urgent need of a composition with the content of "making tea", about 100 words actions:boil water ,take out teapot,prepare era leaves,pour boiled water into erapot,steep a moment before drinking
Looks far long cannot see you,your indignation,where flies?In the fog flies,the imagination dark night after the county let alone to ,do not let me be sad,only then said is not intentionally,I actually am unable to blame you..let alone to not .
－－Prefatory remarks
The year,comes also in a hurry,went in a hurry.has also carried off section of unforgettable recollections,actually left behind sound sad sorry.me to me calmly to lie prone in front of the window,the eye dull dull looks in front of the window all was beautiful,my heart,really the cold.this kind of feeling was such pain.
Do you,why have like this?Has kept why only a note to me,why doesn't come earlier to tell me?On paper sorry,what also can represent?No,don't I want this sorry.leave behind it,what I really cannot make.actually ,I want to detain,only is this pure friendship.not right?Friendship this kind of thing,likes cup of cool boiling water.not to need to add on the sugar,let us drink has felt joyful.therefore ,I drank have been used to the kind of delicacy friendship green tea,disliked these not not really actually to have the sweet taste the syrup,the drink,more repugnant coffee.I did not want you to remain for mine some simple things,perhaps,said to you,only could use to explain with me,but, I did not want,I did not need these.
I,a sentimental girl.ordinary day,has your this and I melts into with the warm heart in the same place,then makes me feel many somewhat is warm and in the regards.life ,I really cannot lack between us this friendship.I continuously all to treat as you the best friend to regard,therefore,I really need between us this friendship ．．．．．．
Did you,really too make me be disappointed.let alone sorry,what sorry cannot leave behind.you to me why with me to say not in front of has walked?Facing front is constructing on the work site rumbling the sound,my heart,more chaotic ．
Choose a few
Given the function f (x) = log21 MX / X-1, the image is symmetric about the origin
(1) The image of the function f (x) = log 2 [(1 – MX) / (x – 1)] is symmetric about the origin, which shows that the function f (x) is an odd function, and the domain of definition is symmetric about the origin. The domain of definition of F (x) is: (1 – MX) / (x – 1) > 0 = > (1 – MX) (x – 1) > 0, so if and only if M = - 1, the corresponding f (x) = L
If the minimum positive period of the function f (x) = sinax + cosax (a > 0) is 1, then a symmetry center of its image is ()
A. (−π8，0)B. （0，0）C. (−18，0)D. (18，0)
If f (x) = sinax + cosax = 2Sin (AX + π 4) t = 2 π a = 1, then a = 2 π, so f (x) = 2Sin (2 π x + π 4) Let f (x) = 0, then there is 2 π x + π 4 = 0x = - 18, that is, one of the symmetry centers is (- 18, 0), so C is chosen
The number corresponding to point a on the number axis is - 1. A bug starts from point a and crawls along the number axis at a speed of 5 units per second to point B,
Immediately return to point a along the original road, which takes 9 seconds. Question: (1) what is the unit length of the crawling distance of the bug? (2) what is the corresponding length of point B? Emergency! Quick!
(1) The crawling distance of the insect is: 5 × 9 = 45 unit length
2. If B is on the right side of a, point B corresponds to: 45 △ 2-1 = 21.5
If B is on the left side of a, point B corresponds to: - 1-45 △ 2 = - 23.5
Ask for an English composition about how to make tea, about 10 sentences
How to Make Tea?
Tea is one of the most popular drinks all over the world.In order to make a good tea drink,firstly,you must have to make tea pot and tea cups warmed up with hot water.In this way,tea pot and tea cups can have the same temperature as the tea prior to serving the tea.The next step of it is to use the right tool to put tea,like green tea,into the tea pot.Don ’t use your hands because the tea will absorb foreign smell.The third one is to put hot water into the tea pot.And then cover the tea pot and use hot water to warm up the lid.You just wait for only a few minutes for the completion of making tea drink.In the next step, you have to wipe the water around the tea pot with towel prior to pouring the tea into the tea cups.Finally ,prior to pouring tea into tea cups,you can put the tea cups in a line, then pour tea into the tea cups and move tea pot back and forth along tea cups to ensure that the flavor is distributed for each individual tea cup.And relax and enjoy your delicious cup of tea.
Given function f (x) = log2 (x-3) + 1 / (x + 2)
Finding the domain of function
Find the value of F (4), f (7 / 2)
The logarithm is significant and the true number is more than 0
x-3>0 x>3
The denominator ≠ 0
x+2≠0 x≠-2
In conclusion, x > 3, the domain of function is (3, + ∞)
f(4)=log2(4-3) +1/(4+2)=0+1/6=1/6
f(7/2)=log2(7/2 -3)+1/(7/2 +2)=log2(1/2)+ 2/11=-1 +2/11=-9/11
The maximum value of the function f (x) = sin2x + cos (2x - π / 6) in the interval [0, π / 2] and the corresponding x value
f(x)=sin2x+cos2xcosπ/6+sinπ/6sin2x
=sin2x+cos2x*√3/2+1/2sin2x
=3/2sin2x+√3/2cos2x
=√3sin(2x+π/6）
0≤x≤π/2
π/6≤2x+π/6≤7π/6
So the maximum value is when 2x + π / 6 = π / 2, that is, when x = π / 6
Take the maximum value √ 3