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Solution: (1)f(x)=3x+2,x<1
f(x)=x²+ax,x≥1
f(f(0))=f(3*0+2)=f(2)=2 +2a=4a, which can be solved: a=2, choose c
2) f(x)=1+x (1-x), this function is a fraction function, as long as the denominator is not zero, 1-x≠0, x≠1
f(f(x)), this function is f(x) in parentheses, that is, f(f(x)) defines the domain as 1+x(1-x)≠1, which gives x≠0 and x≠1
Note: The domain of f(f(x)) can be defined in parentheses as x. of the original function
From the above, it can be seen that a and b = a, choose b.
Hope to understand.
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9.From 0<1, so f(0)=2, by 2>=1, f(f(0))=f(2), 4+2a=4a to get a=2 to choose c
10 Your function is not clearly expressed.
Define the field a as x is not equal to 1
y=f(f(x))=(2/(1-x))*1-x)/(-2x))=-1/x
b defines the field x as not equal to 1 and 0
A and b are unequal to x by 1, that is, a
A crosses b for x is not equal to 1 and 0, that is, b is chosen so b
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9、f(0)=3*0+2=2,f(f(0))=f(2)=2*2+a*2=4+2a=4a
a=210, f(x) defines the domain where x is not equal to 1, and the definition domain b must also meet this condition, choose b
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Question 1: Since there is an arbitrary solution, then if the shilling x=2, then the original formula is equal to: m+2=-m, find m=-1, and let x=1, then 2=n-m
Since m=-1, n=1, then m to the power of 2011 = -1 and n to the power of 2011 = 1
Question 2: a=(2-y) y=2 y-1, bring in 2ax=(a-1)x+6, and get x=3y, so there are countless solutions.
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1. Solution:
As shown in the figure, the color triangle is analyzed, and the meaning is easy to know from the title: the hypotenuse is m (green), the right angle is m 2 (red), and the other right-angled side is obtained by the Pythagorean theorem: 3 2m long. Therefore 1=53°, the same is true for 2=53°, 1+ 2) 2=53°
In summary, the circumferential angle of the chord is 53°
2. Solution: As shown in the figure, it is easy to know from the title: the top angle is 56°, and the bottom angle is 62°; Side 1, side 2, side 3, side 4 are all radius, so side 1 = side 2 = side 3 = side 4, we get three isosceles triangles, in the isosceles triangle composed of side 1 and side 2, 1 = 68°, the same way 3 = 56°, 1 + 2 + 3 = 180°, so 2 = 56°
To sum up, the degrees of the three arcs are 68°, 56°, and 56° respectively.
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I also have to write the title, which is too troublesome, but in fact it is very simple.
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1.Connecting the center of the circle to the three intersections is a square, so it is 90 degrees 2 more complicated.
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Question 1: A's velocity is a, B's velocity is b, and when A reaches the destination, B walks halfway to the destination, then a=8b; The time of the encounter is x by 8 8 at 8 8: bx=8ab 8 8:
bx=8b(x-8) From 8 formula, x=8 is substituted into 8 formula, 9b=ab Therefore: from: A to the purpose.
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1.Let the set m=, n=, if m n, find the range of the value of m.
Solution: For m x1x2=6 and because m n
x1+x2=m
So x1 and x2 can only be 1,6 or 2,3
So m=7 or 5
2.set a=,b=,and a=b,find the value of x,y.
Because a=b
There is an element in b that is 0
So type a also has to have an element of 0
It can only be x-y=0
Because if x=0 or xy=0 then there are duplicate elements in the heads of the tabernacle in a and b, so x=y
a= b=so x 2=|x|
x^2-|x|=0
When x>0, the above equation =x(x-1)=0
Because x is not equal to 0, x=1
At this time, x=1 xy=1 so the element is repeated, excluded.
When x>0, the above equation =x(x-1)=0
So x=-1
At this point a= b=
So x=y=-1
I'm sorry x=y=1 doesn't match, Xie Lou on the chain trillion number correction ,......
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1.First of all, (-m) 2-24>0 i.e. m 2>24 m> 24 under the root number, and m is included in n, so m=6
2.From the meaning of the title, we can see that x≠0 y≠0 so x-y=0 If x =x, then the family is cautious x=0 does not meet so xy= slow x
x=y can disturb the spike to get x=y=-1
The above answer is obviously incorrect.
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1 (-m) type Qing 2-24>0
m^2>24 m>
24 under the root number and m are included in n, so m=6
2.From the meaning of the title, x≠0 y≠0
The rented limb sold is in the Middle Ages x-y=0
If x =x then x=0 does not match.
So xy = x
x=y can be solved to x=y=-1
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4-2*x>0
4-(1/2)^x>0
Separately solved. x<2x>-2
Synthetically -2 defines the domain as (-2,2).
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4-2x>0 so: x<2
0 so:x>-2
x belongs to (-2 ,2).
Question 2: The first question is an odd function because f(x)=-f(-x).
Question 2: Original formula = 1-2 (a x+1) Because a>1, a x belongs to 0 to positive infinity.
So 2 (a x+1) belongs to 0 to 2
So the original form belongs to (-1,1).
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1.Use the scale, first put a bag of candy at one end of the scale, use this bag of candy as the weight (weight), weigh the remaining two bags to find out.
2.If you know whether the defective product is heavy or light, you can weigh it twice, put one on both sides of the scale at the same time each time, find out the different kind of time, and then take off the one that has just been put on one side, and replace the other one, if the scale is balanced, then take down which is defective, if the scale is unbalanced, then the other side is defective.
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Solution: 3 + 2 get.
19x=114
x=6 substitute x=6 into it.
18+4y=16
y= The solution of the original system of equations is.
x=6y=solution: obtained by .
5x+3y=15③
5x-3y=15 is obtained by
Get. 10x=30
x=3 substitutes x=3 into it.
15+3y=15
y=0 The solution of the original system of equations is.
x=3y=0
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Wait, I'll draw you a picture.
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1.Because a=1, c=0, so f(x)=x 2+bx 1, that is, f(x)-1 0, that is, x 2+bx-1 0, and then the main dimension is reversed, and b is regarded as the main element, and x is regarded as the dimension, that is, x is known, so it becomes a one-dimensional inequality about b, because x (0, 1, so the inequality is brought in, -1 0 is constant, 1 2+1 b-1 0, and b 0, in summary, b 0 2That is, 4 x + m (2 x) + 1 = 0 holds, and the equal sign shifts both sides, that is, m=-(2 x+2 -x), that is, find the range of f(x) = -(2 x+2 -x), because x r, so (2 x) (0, + commutation, so that 2 x=t, t (0, + i.e., the original formula is y=-(t+1 t), and y (-2) is obtained from t, that is, m (-2).