If we know that the image of the function f (x) = | 2x-1 | has two common points with the line y = a, then the value range of a is______ ．

If we know that the image of the function f (x) = | 2x-1 | has two common points with the line y = a, then the value range of a is______ ．

The image of F (x) = | 2x-1 | is shown in the figure below: it can be seen from the figure that when 0 < a < 1, the image of function f (x) = | 2x-1 | has two common points with the line y = a, so the answer is: (0, 1)

To solve some problems of solving function analytic expressions in senior one mathematics
For example, if we know f [f (x)] = 2x - 1, we can find the analytic expression of the first-order function f (x)
I want to find some more to practice

Let f (x) = ax + B
f[f(x)]=af(x)+b=a(ax+b)+b=2x-1
A = + - radical 2
B = - + (radical 2-1)

English translation
and,array,call,constant,else,elseif,endfunction,endglobals,endif,endloop,exitwhen,extends,function,globals,if,local,loop,native,not,or,return,returns,set,takes,type,then
These are the words. Just write down the general meaning. Polysemous words should be noted

Array, phone, and others, if not, or local, back, back, back, set, type, and then

It is proved that the sequence {an} is an arithmetic sequence if and only if the sum of the first n terms of the sequence {an} is Sn = an & # 178; + BN (where a and B are constants)

Proof: sufficiency:
sn=an²+bn
sn-1=a(n-1)²+b(n-1)
So an = sn-sn-1 = an & # 178; + BN - [a (n-1) &# 178; + B (n-1)] = 2an-a + B = (a + b) + (n-1) * 2A = a1 + (n-1) d
So an is an arithmetic sequence with a + B as the first term and a tolerance of 2A
Necessity: let an = a1 + (n-1) d = (a1-d) + nd
Then Sn = n (a1-d) + D * n (n + 1) / 2 = 1 / 2 * DN ^ 2 + (a1-d / 2) n = an ^ 2 + BN
Where a = D / 2, B = a1-d / 2
So the sequence {an} is an arithmetic sequence if and only if the sum of the first n terms of the sequence {an} is Sn = an & # 178; + BN (where a and B are constants)

Let X & sup2; + xy = 3, XY + Y & sup2; = 2, find the value of 2x & sup2; - xy-3y & sup2

2x²－xy－3y²
=2x²+2xy-2xy－xy－3y²
=2x²+2xy-3xy－3y²
=2(x²+xy)-3(xy+y²)
x²＋xy=3,xy＋y²＝2
Bring in
2*3-3*2=0

The coal transported by car in the second time is 28 tons less than that in the first time. The coal transported in the second time is 0.8 times of that in the first time. How much coal are transported in two times

Suppose that the first coal transportation is x tons, then the second coal transportation is 0.8x tons. The one variable equation x-0.8x = 28 is listed, and 0.2x = 28 is obtained by solving the equation
Therefore, the first coal transportation is 140 tons, and the second coal transportation is 112 tons
It is also possible to list the solutions of the system of linear equations of two variables

As shown in the figure, how many pairs of vertex angles are there when three straight lines intersect each other? How many pairs of complements? How many pairs of apposition angles? How many pairs of wrong angles? How many pairs of inner corners on the same side?

There are 6 pairs of vertex angle, 12 pairs of complementary angle, 12 pairs of apposition angle, 6 pairs of internal stagger angle and 6 pairs of internal angle

There is a question, f (- 1) = 0, f (1) = 0, but it is proved that the function is odd. Why f (XY) = y * f (x) + X * f (y)
No, I mean why f (x) = f (- x) isn't that an even function? Or why can an odd function f (1) = f (- 1) = 0

Let x = y = 1
The original formula becomes f (1) = f (1) + F (1) = 2F (1) = > F (1) = 0
Let y = - 1 be substituted
f(-x) = -f(x) + xf(-1)
f(-1) = 0
So f (- x) = - f (x)
So f (x) is an odd function
It's over

What are the physical properties of water and sugar?
Write the physical properties of water and sugar respectively
It's not a physical change

The physical properties of water are: colorless transparent liquid, density 1g / cm3, weak conductivity, melting point 0 ℃, boiling point 100 ℃
Sugar physical properties are: white transparent crystal, density (table), weak conductivity, melting boiling point (table), solubility: soluble in water

Explanation of the formula and process of solving the problem of cattle grazing

Y = (N-X) × T, where y represents the original stock (such as the original grass quantity), n represents the exogenous variable (such as the number of cattle) that causes the original stock to decrease, X represents the natural growth rate of the stock (such as the grass growth rate), and t represents the time taken for the stock to disappear completely