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Given that the function f (x) satisfies 3f (x) + 2F (- x) = 2x + 2, the analytic expression of F (x) is obtained
Let x = - X
Then 3f (- x) + 2F (x) = - 2x + 2
Solve the equations 3f (x) + 2F (- x) = 2x + 2,3f (- x) + 2F (x) = - 2x + 2
So, f (x) = 2x + 0.4
It is known that f (x) is a quadratic function and satisfies 3f (x + 1) - 2F (x-1) = x ^ 2 + 2x + 17
Undetermined coefficient method: Let f (x) = ax ^ 2 + BX + C, then f (x + 1) = a (x + 1) ^ 2 + B (x + 1) + C = ax ^ 2 + X (2a + b) + A + B + CF (x-1) = a (x-1) ^ 2 + B (x-1) + C = ax ^ 2 + X (- 2A + b) + A-B + C3F (x + 1) - 2F (x-1) = ax ^ 2 + X (10a + b) + A + 5B + C = x ^ 2 + 2x + 17. By comparing the coefficients, a = 1,10a + B = 2, a + 5B + C = 17
The equation of a line which is parallel to the line 2x + 3Y + 5 = 0 and whose sum of intercept on the two coordinate axes is 6 is______ ．
Suppose that the linear equation is 2x + 3Y + C = 0, let x = 0 get y = − C3, let y = 0 get x = − C2, ■ − C3 − C2 = 6, let C = − 365, let 2x + 3y-365 = 0, let x = 0 get y = − C3, let y = 0 get x = − C2, ■ − C3 − C2 = 6, let C = − 365, let 2x + 3y-365 = 0, let x = 0 get 10x + 15y-36 = 0, so the answer is: 10x + 15y-36 = 0
How to use a simple method to calculate 2 * 1 / 7 + 7 * 1 / 12 + 12 * 1 / 17 + 17 * 1 / 22?
2*1/7+7*1/12+12*1/17+17*1/22
=2/7+7/12+12/17+17/22
=(1-5/7)+(1-5/12)+(1-5/17)+(1-5/22)
=4-5(1/7+1/12+1/17+1/22)
=4-5[29/(7*22)+29/(12*17)]
=4-145(1/154+1/204)
=4-145[(102+77)/(77*2*102)]
=4-25955/15708
=2.5461/15708
The line y = 2x + B intersects with the X, Y axis at the points a, B and O, where the two points are the origin and the triangle AOB area is 9
6
b/2 * b * 1/2 =9
b=6
Find (2x-1) / (1-3x) domain and range
Please write a clear process of problem solving, I want to process
Domain of definition: solve the inequality 1-3x ≠ 0 to get x ≠ 1 / 3
Range: y = (2x-1) / (1-3x)
y-3yx=2x+1
2x+3yx=y-1
x(2+3y)=y-1
x=(y-1)/(2+3y)
The domain of the function with y as the independent variable is y ≠ - 3 / 2
According to the fact that the domain of inverse function is the domain of original function, the domain of known function is y ≠ - 3 / 2 (in the form of set)
Cut a 60cm cuboid into three sections, and the surface area will be increased by 80 square centimeters. What is the volume of this cuboid?
If the cuboid is cut into three sections, the surface area will increase by four sections
A cross-sectional area = 80 △ [(3-1) × 2] = 20 square centimeters
Cuboid volume = 20 × 60 = 1200 cm3
It is known that the equation AX ^ 2 + 4x + a = 1-2x ^ 2 about X has two unequal real roots, then the value range of real number a is
Ax ^ 2 + 4x + a = 1-2x ^ 2 (a + 2) x ^ 2 + 4x + A-1 = 0 because the equation AX ^ 2 + 4x + a = 1-2x ^ 2 has two unequal real roots, so a + 2 ≠ 0, Δ = 4 ^ 2-4 (a + 2) (A-1) > 0, so a ≠ - 2, a ^ 2 + a-6 < 0, that is (A-2) (a + 3) < 0, so - 3 < a < 2 and a ≠ - 2, so the value range of real number a is {a | - 3 < a < 2
If a = 13, B = - 21.1, C = - 10.1, then the sum of - A-B + C = (2) - 7, - 12,2 is smaller than the sum of their absolute values
Well, what grade of children
1.-a-b+c=-13-(-21.1)+(-10.1)=-13+21.1-10.1=-2
2. The sum of - 7, - 12,2 = - 7 + (- 12) + 2 = - 7-12 + 2 = - 17
Sum of absolute values = | - 7 | + | - 12 | + | - 2 | = 7 + 12 + 2 = 21
When the function sinxcosx + SiNx + cosx, FX takes the maximum value, the set of X
Sinxcosx = 1 / 2 sin (2x), the maximum value is 1 / 2, when 2x = 2K π + π / 2, that is, x = k π + π / 4
SiNx + cosx = √ 2Sin (x + π / 4), the maximum value is √ 2, which is obtained when x + π / 4 = 2K π + π / 2, that is, x = 2K π + π / 4
Therefore, the maximum value of the function is 1 / 2 + √ 2, which is obtained when x = 2K π + π / 4, where k is an arbitrary integer
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