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Given the function f (x) = AX2 + BX + C, if f (0) = 0, f (x + 1) = f (x) + X + 1, find the expression of F (x) AX2 is the power of X
f(x)=ax²+bx+c∵f(0)=0∴c=0∴f(x)=ax²+bxf(x+1)=a(x+1)²+b(x+1)=ax²+2ax+a+bx+b=ax²+(2a+b)x+a+b=f(x)+x+1∴ax²+(2a+b)x+a+b=ax²+bx+x+1ax²+(2a+b)x+a+b=ax²+(b+1)x+...
Find the range of the following functions
1) y= √(x)+1
(2)y=x^2-4x+5
(3)y=x^2+2x+3
("√" means under the root sign, and √ (x) means x under the root sign)
(1)
y∈[1,+∞)
(2)
y=(x-2)^2+1
y∈[1,+∞)
(3)
y=(x+1)^2+2
y∈[2,+∞)
A very simple question
If | cosx | = cos (- x + π), then the value range of X is
According to the induction formula: cos (- x + π) = - cosx
So | cosx | = - cosx
∴cosx≤0,
2kπ+π/2≤x≤2kπ+3π/2.k∈Z
Is there a functional relationship between the following quantities? Why?
(1) A square has a certain side length, its perimeter and area;
(2) Trapezoid has a certain upper bottom length, and its lower bottom length is related to its area
(1) Perimeter: y = 4x (x is side length, y is perimeter) positive proportional function
Area: y = x & sup2; (x is side length, y is area) quadratic function
(2) Seems not high, angle. Can't calculate the bottom length and area, should not exist
A function problem in the second year of junior high school,
If we know the first-order function y = KX + B, when x decreases by 9, y increases by 3 instead, then K
y+3=k(x-9)+b (1)
y=kx+b (2)
Set up a system of equations
Equation 1 minus equation 2
3 = - 9K
k=-1/3
The intersection of the functions y = - X and y = 2x + 3 is_______
(- 1,1) y = - X and y = 2x + 3 are combined to form a system of equations. The solution of the system of equations is x = - 1, y = 1. The intersection point can also be found by drawing
It is known that the value range of the independent variable x in the function y = KX + B is - 2 ≤ x ≤ 6, and the function y is - 22 ≤ y ≤ 18
When x = - 2, y = - 22, x = 6, y = 18 is substituted by - 2K + B = - 226k + B = 18, the solution is k = 5B = - 12, i.e. y = 5x-122. When x = - 2, y = 18, x = 6, y = - 22 is substituted by - 2K + B = - 186k + B = - 22K = - 5B = 8, i.e. y
Given the function y = Y1 + Y2, where Y1 is positively proportional to the square of X and Y2 is inversely proportional to X. when x = 1, y = 1; when x = 3, y = - 17. Find the value of y when x = - 1
If Y1 is positively proportional to the square of X, then Y1 = MX & # 178;
Y2 is inversely proportional to x, y2 = n / X
y=y1+y2 = mx²+n/x
When x = 1, y = 1, then M + n = 1
When x = 3, y = - 17, then 9m + n / 3 = - 17
Simultaneous solution
m=-2,n=3
therefore
When x = - 1, y = MX & # 178; + n / x = M-N = - 2-3 = - 5
50 more points! Sit down and wait
A straight line in the plane can divide the plane into two parts, and two straight lines can divide the plane into four parts at most. How many parts can n straight lines divide the plane into? Is the result a function of N? If it is, please write the function, but not the reason +n=1/2 n（n+1） ）
Can be divided into 2n parts, of course, is a function of n
In fact, mathematics is not so complicated. This is a question to fill in the blanks
Simple second function problem. Fast
1. It is known that the circumference of an isosceles triangle is 36, the waist length is x, and the height of its bottom is 6. If the area y is regarded as a function of the waist length x, try to write out the functional relationship between Y and X, and find out the value range of X
2. The car drives from Beijing to Shenyang 840km away. The speed of the car is 70 km per hour. After t (H), the car is s (km) away from Shenyang
(1) Find the functional relationship between S and T, and write out the value range of independent variable t
(2) How many kilometers is the car from Shenyang after 2 (H)?
(3) How many hours later, the car is 140 kilometers away from Shenyang?
3. When x = (), the value of function y = 27x + 3 is the same as that of function y = 2x-7, which is ()
Hurry up. Thank you. Help. I need it urgently
1) y=6*(36 -2X)=216-12X
0
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