Mathematical function problem? 1. A factory produces one kind of parts, and the daily income is 28 yuan when the quota is fulfilled. If one part is overproduced and the income is increased by 1.5 yuan, then the functional relationship between a worker's daily income y yuan and the number of overproduced parts x is () 2. A factory has 800 tons of coal and burns 5 tons of coal every day. Find out the functional relationship between Y tons of surplus coal and X days of burning coal, and point out whether y is a linear function of X 3. Under normal circumstances, the maximum number of heart beats per minute (s / min) a person can bear during exercise is a function of the person's age of N years (1) According to the following information, the function of s with respect to n is obtained under normal conditions. According to the surface of scientific research in medicine, the heart rate of people during exercise is usually related to their age. Under normal conditions, the maximum heart rate that people aged 15 and 45 can bear during exercise is 164 beats / min and 144 beats / min respectively (2) If a 63 year old man is running and the doctor measures 26 beats in 10 seconds on the way, ask: is he in danger? Why? 4. It is known that y + m is in direct proportion to x-m (where m and N are constants). If x = - 1, y = - 15; X = 7, y = 1, find the relationship between Y and X 5. In the activity of Yunnan green hope project, the action of protecting mother river, a kind of telephone card was issued. The purpose is to build ten thousand mu of young people's new century forest at the beginning of the new century. The face value of this kind of telephone card is 12 yuan, of which 10 yuan is the call fee, 2 yuan is donated to Yunnan green hope project fund, and 1 yuan is attached to the call fee, Yunnan green hope project fund is the function y (1) Write the function relation between Y and X, and find the value range of the independent variable x (2) It is known that the cost of planting trees per mu is 400 yuan. If there are 46000 junior high school graduates in our city this year, and each person buys a card, how many mu of trees can the fund plant?

Mathematical function problem? 1. A factory produces one kind of parts, and the daily income is 28 yuan when the quota is fulfilled. If one part is overproduced and the income is increased by 1.5 yuan, then the functional relationship between a worker's daily income y yuan and the number of overproduced parts x is () 2. A factory has 800 tons of coal and burns 5 tons of coal every day. Find out the functional relationship between Y tons of surplus coal and X days of burning coal, and point out whether y is a linear function of X 3. Under normal circumstances, the maximum number of heart beats per minute (s / min) a person can bear during exercise is a function of the person's age of N years (1) According to the following information, the function of s with respect to n is obtained under normal conditions. According to the surface of scientific research in medicine, the heart rate of people during exercise is usually related to their age. Under normal conditions, the maximum heart rate that people aged 15 and 45 can bear during exercise is 164 beats / min and 144 beats / min respectively (2) If a 63 year old man is running and the doctor measures 26 beats in 10 seconds on the way, ask: is he in danger? Why? 4. It is known that y + m is in direct proportion to x-m (where m and N are constants). If x = - 1, y = - 15; X = 7, y = 1, find the relationship between Y and X 5. In the activity of Yunnan green hope project, the action of protecting mother river, a kind of telephone card was issued. The purpose is to build ten thousand mu of young people's new century forest at the beginning of the new century. The face value of this kind of telephone card is 12 yuan, of which 10 yuan is the call fee, 2 yuan is donated to Yunnan green hope project fund, and 1 yuan is attached to the call fee, Yunnan green hope project fund is the function y (1) Write the function relation between Y and X, and find the value range of the independent variable x (2) It is known that the cost of planting trees per mu is 400 yuan. If there are 46000 junior high school graduates in our city this year, and each person buys a card, how many mu of trees can the fund plant?

1 y = 28 + 1.5x2 y = 800-5x3 (1) let y = KX + B (k is not equal to 0) substitute (15164) (45144) into the solution of y = KX + B {164 = 15K + B 144 = 45k + B to get {k = - 2 / 3

Function f (x) = root sign (square of a * x + BX + C) where a

If all the points (s, f (T)) (s, t ∈ d) form a square, then the length of X and the length of range are equal
Length of X of domain = | x1-x2 | = √ [(x1 + x2) ^ 2-4x1x2]
=√[(-b/a)^2-4c/a]
=√[(b^2-4ac)/a^2]
The length of the range is from 0 to the maximum, which is √ [- B ^ 2 / (4a) + C]
√[-b^2/(4a)+c]=√[(b^2-4ac)/a^2]
So there is (b ^ 2-4ac) / A ^ 2 = (4ac-b ^ 2) / 4A
We get a ^ 2 = 4A
a

Let FX = a (x-1 / x) - LNX
(1) When a = 1, find the tangent equation of curve y = FX at point (1, f (1))
(2) if the function y = FX is an increasing function in its domain of definition, find the value range of real number a

First, the tangent point (1,0) & nbsp; is derived from F (x), F & # 39; (x) = (x ^ 2-x + 1) / x ^ 2 & nbsp; & nbsp; to get the slope k = 1L & nbsp;: y = X-1 to get F & # 39; (x) = (AX ^ 2-x + a) / x ^ 2 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; the definition field is (0, positive infinity)

Mathematical function problems... Urgent!
As shown in the figure, it is known that the image of the first-order function y = x + 1 and the image of the inverse scale function y = K / X intersect at point a in the first quadrant, intersect with the X axis at point C, AB is perpendicular to the X axis at point B, and the area of the triangle AOB is 1, then the length of AC is
Here's the picture
Now I have worked out a (1,2) and then how to calculate it? Do I need to calculate the coordinates of point C? How to calculate the coordinates of point C? Who will tell me... Urgent... (I'm afraid no one will answer. So I didn't give any points

It's very simple that C is the intersection of a linear function and the X axis, so the ordinate of C is 0, that is, y equals zero, so C is (- 1,0), BC length is 2, AB length is 2, and because the angle ABC is a right angle, we can find AC by Pythagorean theorem

A periodic function problem, for help!
For a function defined on R, f (x) satisfies f (- x) = - f (x), f (1-x) = f (1 + x). When x is in [- 1,1], f (x) = X3, then the value of F (2007)
But there is one step in the answer: F (x) = - f (x) = - f (x + 2),
Is the first step derived from F (1-x + 1) = f (1 + X + 1) and the second step?
Its period is 4. Can we use its method?

In F (1-x) = f (1 + x), substituting x = 1 + X into f (- x) = f (2 + x) and f (- x) = - f (x), there is - f (x) = f (2 + x), that is, f (x) = - f (2 + x). There is a mistake in the step you gave, which should be f (x) = - f (- x) = - f (x + 2)

A question about periodic function~
Let f (x) be a function with a period of 4 and an odd function. We know that when x is less than or equal to 2 and greater than or equal to 0, f (x) = the square of 2x-x, find the expression of F (x) on [- 2,6] ~ how to solve this problem? We started to learn advanced mathematics today. I have lost mathematics for half a year, and I have nothing left

When x ∈ [0,2], f (x) = 2x-x ^ 2
Because f (x) is an odd function, when x ∈ [- 2,0], f (x) = - f (- x) = - [2 (- x) - (- x) ^ 2] = 2x + x ^ 2
Because f (x) has a period of 4, when x ∈ [2,6], f (x) = f (x-4), where we subdivide:
When x ∈ [2,4], f (x) = f (x-4) = 2 (x-4) + (x-4) ^ 2 = x ^ 2-6x + 8
When x ∈ [4,6], f (x) = f (x-4) = 2 (x-4) - (x-4) ^ 2 = - x ^ 2 + 10x-24
In conclusion, in the interval [- 2,6], f (x) is the following piecewise function
f(x)=2x+x^2,x∈[-2,0]
f(x)=2x-x^2,x∈[0,2]
f(x)=x^2-6x+8,x∈[2,4]
f(x)=-x^2+10x-24,x∈[4,6]

Ask a question about the periodicity of functions
The function f (x) is a function with period of 2 π. When x ∈ [- π, π), f (x) = X. when x ∈ [2m π - π, 2m π + π) (m ∈ z), the expression of function f (x) is obtained
Can you give the process of solving the problem

The function f (x) has a period of 2 π, that is, f (x) = f (x + 2 π)
So when x ∈ [2m π - π, 2m π + π), x-2m π ∈ [- π, π)
So f (x-2m π) = f (x) = x-2m π
The expression bit of function f (x) = x-2m π

1. What is the minimum positive period of the function y = SiNx + cosx
2、 The focus coordinate of parabola y * y = - 8x is? 3: choose four from five boys and four girls to participate in the activity, of which there are at least two boys and at least one girl. How many choices are there?

1 y=sinx+cosx=√2sin(x+π/4)
Minimum positive period T = 2 π / 1 = 2 π
2 focus (- 2,0)
3 C(2,5)C（2,4）+ C(3,5)C（1,4）
=60+40=100

On the mathematical problems of periodic function
F (x) = √ 3sinxcosx + cos ^ 2x-1 / 5 (x belongs to R)
(1) Finding the period of function f (x)
(2) Finding the increasing interval of function f (x)

（1）f（x）＝√3/2sin2x+1/2cos2x+1/2-1/5
＝sin（2x+∏/6）+3/10
So the period T = 2 Π / 2 = Π
(2) When 2K Π - Π / 2 ≤ 2x + Π / 6 ≤ 2K Π + Π / 2
That is, when k Π - Π / 3 ≤ x ≤ K Π + Π / 6 (k is an integer)
F (x) monotonically increasing
When 2K Π + Π / 2 ≤ 2x + Π / 6 ≤ 2K Π + 3 Π / 2
That is, when k Π + Π / 6 ≤ x ≤ K Π + 2 Π / 3 (k is an integer)
Monotonic decreasing of F (x)

A mathematical problem about the period of function
f(x-4)= -f(x)
The answer is f (x + 8) = f (x), so the period is 8
I don't understand

Because f (x-4) = - f (x), f (X-8) = f ((x-4) - 4) = - f (x-4) = - [- f (x)] = f (x), so f (x + 8) = f ((x + 8) - 8) = f (x), so the period is 8