![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
It is known that the domain of definition of functions f (x) and G (x) is r, where f (x) is odd, G (x) is even, and f (x) + G (x) = 1 / (the square of x-x + 1) Finding the analytic expressions of F (x), G (x)
Let H (x) = f (x) + G (x)
h(x)+h(-x)= f(x)+g(x)+f(-x)+g(-x)=2g(x)
h(x)-h(-x)= f(x)+g(x)-f(-x)-g(-x)=2f(x)
So it's very simple: H (x) + H (- x) divided by 2 to get g (x)
Divide H (x) - H (- x) by two to get f (x)
It is known that f (x) is an odd function, G (x) is an even function, f (x) + G (x) = LG (x + 1)
1. Find f (x) and G (x). 2. If G (x) is less than a in the domain of definition, find the range of A
（1） It is easy to know that f (x) + F (- x) = 0. G (x) = g (- x) (- 1 ＜ x ＜ 1). F (x) + G (x) = ㏑ (x + 1), f (- x) + G (- x) = ㏑ (1-x & sup2;). By adding the two formulas, G (x) = ㏑ √ (1-x & sup2;). By subtracting the two formulas, f (x) = ㏑ √ [(1 + x) / (1-x)]. (- 1 ＜ x ＜ 1). (2) g (x) = ㏑ √ (1-x & sup2;) ＜ a, (- 1 ＜ x ＜ 1)
The product of 19 and () is prime
A:
The product of 19 and (1) is prime
It must not be multiplied by a number greater than 1, otherwise it is not prime
Because the result of multiplication is prime = 19 * X
Then the prime factor can only be 19 and 1
Some problems of function image in junior high school mathematics
1. Given the points M1 (- 1, - 2), M2 (- 2, - 1), m3 (1,2), M4 (2,1), which are not on the graph of function y = x + 1, there are -
2. If the point (- 2,3) exists on the image of function y = 2x + 2m, then M = --
3. If the point (- 6, a under the root sign) is on the image of the function y = 2x & # 178; - 1, then a = --
4. If the image of a function is in one or two quadrants, then the value of the function ()
A. All integers B. all negative numbers C. all non negative numbers D. can be positive or negative or 0
5. Given that point (3,6) is on the graph of function y = K / X (K ≠ 0), then the following points are ()
A.（-3,6） B.(2,9) C.(2.-9) D.(3.-6)
1. Given the points M1 (- 1, - 2), M2 (- 2, - 1), m3 (1,2), M4 (2,1), which are not on the image of function y = x + 1 are: M1, M4.2, if the point (- 2,3) exists on the image of function y = 2x + 2m, then M = 3.5.3, if the point (- 6 under the root sign, a) exists on the image of function y = 2x & # 178; - 1, then a = 11.4, if a function
As shown in the figure, it is known that the line AB = 10, AC = BD = 2, and point P is a moving point on CD. Take AP and Pb as edges, make squares APEF and phkb up and down respectively. Let the intersection points of the square diagonals be O1 and O2 respectively. When point P moves from point C to point D, the length of the motion path of point G in line O1O2 is___ ．
As shown in the figure: when P moves to point C and point D, it is concluded that the moving route of point G is a straight line. By using the properties of square, that is, the length of the moving path of point G in line O1O2 is the length of o2o ″, ∵ line AB = 10, AC = BD = 2, when p coincides with C, take AP and Pb as edges, make square APEF and phkb upward and downward, ∵ AP = 2, BP = 8, then o1p = 2, o2p = 42, ∵ o2p = o2b = 42, when p ′ coincides with D, Then p ′ B = 2, AP ′ = 8, O ′ P ′ = 42, O ″ P ′ = 2, H ′ o ″ = Bo ″ = 2, o2o ″ = 42-2 = 32
The minimum natural number of digits 1 or 0 in 10 system and divisible by 225
Such as the title
The answer is 100 * (10 Λ 9-1) / 9
225 = 15 * 15 = 9 * 25
Because this number only contains the number 0 or 1, it can be divided by 225, that is, it can be divided by 9 and 25. According to the characteristics of the number that can be divided by 9 (it should be the sum of all numbers that can be divided by 9)
Therefore, the number contains at least nine ones,
And because it's divisible by 25, it's a multiple of 100
That is, the number is equal to 11100 = 100 * (10 ^ 9-1) / 9
Let the random variables XY be independent of each other and obey the uniform distribution of (0.1)
FZ (z) = ∫ (∞→ + ∞) FX (x) FY (z-x) DX (1) Z < 0fz (z) = ∫ (∞→ + ∞) FX (x) FY (z-x) DX = 0 (2) 0 ≤ Z < 1fz (z) = ∫ (0 → Z) 1.1dx = Z (3) 1 ≤ Z < 2fz (z) = ∫ (0 → Z-1) 1.0dx + ∫ (Z-1 → 1) 1.1dx = 2-z (4) Z ≥ 2, FZ (z) = ∫ (∞→ + ∞) FX (x) FY (z-x) = ∫ (0 → Z-1) 1.0dx + ∫ (Z-1 → 1) 1.1dx = 2-z (4) Z ≥ 2
Calculation of sin (PI / 7) + ln3-e ^ J * 3 by MATLAB
sin(pi/7)+log(3)-exp(complex(0,3))
Or change the power of e into trigonometric function
sin(pi/7)+log(3)-cos(3)-complex(0,sin(3))
Complex (0,3) stands for imaginary number 0 + J3
Positive 3, negative 5, negative 11, and positive 7 make the result equal to 24 for mixed operation (write one for each time only)
[（＋7）－（＋3）]×[（－5）－（－11）]
＝4×6
＝24
A parallelogram has an area of 36 square meters and a bottom of 9 meters. There is a triangle with the same area and bottom. What is the height of the triangle?
36 × 2 △ 9 = 8 (m)
RELATED INFORMATIONS
- 1. It is known that f (x) is an odd function and G (x) is an even function. When x ≥ 0, f (x) = LG (x + 1); when x < 0, G (x) = f (x), the analytic expression of G (x) when x > 0 is obtained
- 2. Given FX = x square + ax + 1, if it is even function, find a
- 3. If the even function f (x) defined on R monotonically decreases on (- ∞, 0], and f (- 1) = 0, then the solution set of inequality f (x) > 0 is () A. （-∞，-1）∪（1，+∞）B. （-∞，-1）∪（0，1）C. （-1，0）∪（0，1）D. （-1，0）∪（1，+∞）
- 4. For the even function f (x) defined on [- 2,2], when x > = 0, f (x) decreases, then the inequality f (1-x)
- 5. The function y = f (x) defined on R satisfies f (- x) = - f (x), f (1 + x) = f (1-x) when x ∈ (0,1] f (x) = root sign (x + 1), then the value of F (2011) is
- 6. An applied problem of binary linear equations The father gave his son a question and asked him to guess the answer. He said that there was a mother and daughter. Five years ago, the mother's age was 15 times the daughter's; 15 years later, the mother's age was more than twice the daughter's. 6. What's the age of the mother and daughter now?
- 7. Solving applied problems of linear inequalities with one variable A company purchased 40 sets of air conditioners and 60 sets of refrigerators, and allocated them to its two subordinate shopping malls for sale, 70 sets in shopping mall a and 30 sets in shopping mall B. the profits of two kinds of electrical appliances sold by the two shopping malls are as follows: (unit: yuan) Air conditioning refrigerator Department store a 200 170 Shopping mall B 160 150 (1) The company supplies x air-conditioners to a shopping mall. The total profit of the two shopping malls after buying all the electrical appliances is expressed by the algebraic formula of X, and the value range of X is calculated (2) In order to promote the sales, the company decided to give a profit of a yuan to each air conditioner in a shopping mall, but the profit of each air conditioner should not be less than the profit of each refrigerator in a shopping mall?
- 8. Solving a mathematics problem in grade two of junior high school In a village, m HA is planted, and the total yield of corn is n kg; the rice planting area is p ha more than the corn planting area, and the total yield of rice is 2 times more than that of corn. Q kg is used to write the formula of unit area yield of corn and rice [unit; kg / HA]. If the denominators of the two formulas are different, the two formulas are divided
- 9. (hard) A bucket of 30 liters of pure alcohol, pour out a number, fill it with water, and then pour out the same volume, leaving 4.8 liters of pure alcohol. How much pure alcohol is poured out each time? It's a series of equations,
- 10. On the system of linear inequalities of one variable in the second grade of junior high school mathematics Give a basket of oranges to several children. If each child gets 4 oranges, there will be 9 oranges left. If each child gets 6 oranges, the last child gets less than 3 oranges. How many oranges are there?
- 11. How to write a function in the form of an odd function and an even function Take F (x) = x + 1 / (2 + x) as an example,
- 12. Let f (x) be a continuous even function on (- ∞, + ∞), and prove that f (x) = ∫ (0 → x) f (T) DT is an odd function
- 13. Given that f (x) is an even function, G (x) is an odd function, f (x) + G (x) = x ^ 2 + 2 ^ x, find f (1)
- 14. What is "odd function. Even function"? We don't have that in our math books, But there are some problems about odd function and even function Please be more specific
- 15. How to judge whether a function is even or odd
- 16. F (x) = log2 [(1-ax) / (x-1)] odd function a is a constant. 1. Find the value of A. 2. Prove that f (x) monotonically decreases in the interval (1, positive infinity), 3.3. If the inequality f (x) B - (1 / 2) ^ x holds for any value of X on [3,5], find the value range of real number B
- 17. Given that a, B, C are real numbers, f (x) = AX2 + BX + C, G (x) = ax + B, when - 1 ≤ x ≤ 1 | f (x) | ≤ 1. (1) prove: | C | ≤ 1; (2) prove: when - 1 ≤ x ≤ 1, | g (x) | ≤ 2; (3) let a > 0, when - 1 ≤ x ≤ 1, the maximum value of G (x) is 2, and find f (x)
- 18. The relationship between the slope of focus chord and the ratio of focus chord and eccentricity of conic curve? RT
- 19. How to find the locus of the middle point of a line segment whose distance between two points on a conic curve is fixed Take the parabola as an example: Y & # 178; = 2px, (P > 0), a and B are two points on the parabola, and ab = 3, find the trajectory equation of the midpoint m in ab
- 20. The midpoint problem of conic chord To solve the linear equation of the chord of hyperbola with a (m, n) as the midpoint, we can use f (x1) - f (x2) to get the result. But why does it not exist?