The function f (x) = ax + B, a, B ∈ R, when x is greater than or equal to - 1 and less than or equal to 1, the absolute value of F (x) is less than or equal to 1 It is proved that the absolute values of a and B are less than or equal to 1

The function f (x) = ax + B, a, B ∈ R, when x is greater than or equal to - 1 and less than or equal to 1, the absolute value of F (x) is less than or equal to 1 It is proved that the absolute values of a and B are less than or equal to 1

It's very simple
Firstly, when x is greater than or equal to - 1 and less than or equal to 1, the absolute value of F (x) is less than or equal to 1
Then when x = 1, there is | a + B | 1
When x = - 1, there is | B-A | 1
Then | (a + b) + (B-A) | (a + B + | B-A | 2
|2B | 2, there is | B | 1
Similarly, there are | (a + b) - (B-A) | and | a + B | + | B-A | 2
Then | a | 1

Let f (x) = ax + 2, and the solution set of F (x) whose absolute value is less than 6 be (- 1,2)?

If the absolute value of F (x) is less than 6, the solution set is (- 1,2),
We get | ax + 2|

The minimum value of the function y = (x ^ 2-3x + 2) / (x ^ 2 + 2x + 1) is
Extremum and derivative of function

y'=[(2x-3)(x^2+2x+1)-(2x+2)(x^2-3x+2)]/[(x^2+2x+1)^2]=0
Simplify (x + 1) (5x-7) = 0
The solution x = - 1, x = 7 / 5
When x = - 1, the function is meaningless, so x = 7 / 5 is its minimum

Let f (x) = X3 + bx2 + CX, G (x) = f (x) - F ′ (x). If G (x) is an odd function, find the value of B and C

From F (x) = X3 + bx2 + CX, f ′ (x) = 3x2 + 2bx + C, then G (x) = f (x) - F ′ (x) = X3 + (B-3) x2 + (c-2b) x-C, ∵ g (x) is an odd function, ∵ G (0) = - C = 0, C = 0. ∵ g (x) = X3 + (B-3) x2-2bx

If point P (a + 3,3a-2) is in the fourth quadrant and its coordinates are all integers, then the value of a is

If the point is in the fourth quadrant, its abscissa is positive and its ordinate is negative
That is, a + 3 > 0 and 3a-2

How many picoseconds is one millisecond

One picosecond equals one billionth of a second (10-12 seconds)
0.000001 picosecond = 1 μ s
0.001 picosecond = 1 femtosecond
1000 picoseconds = 1 nanosecond
1000000 picoseconds = 1 microsecond
1000000000 picoseconds = 1 millisecond

Given the point P (x, y) on the ellipse X & # 178; / 144 + Y & # 178; / 25 = 1, find the value range of u = x + y?

Since P (x, y) is on the ellipse (X & # 178 / 144) + (Y & # 178 / 25) = 1, let x = 12cosa, y = 5sina, then x + y = 12cosa + 5sina = 13 [(12 / 13) cosa + (5 / 13) Sina] = 13sin (a + θ), where sin θ = 12 / 13, here we use the auxiliary angle formula  x + y ∈ [- 13,13]

Given the function f (x) = 2cos ^ 2x-2 * 3 ^ 1 / 2sinxcosx, find the minimum positive period of (1) function and the minimum value of (2) function

f（x）=2cos^2x-2*3^1/2sinxcosx
=1+cos2x-√3sin2x
=1+2(1/2cos2x-√3/2sin2x)
=1+sin(π/6+2x)
Period 2 π / 2 = π
When the minimum sin (π / 6 + 2x) = - 1, it is 0

If the focus of the straight line x + 2Y + K + 1 = 0 and the straight line 2x + y + 2K = 0 is in the third quadrant, find the value of K
3. Given x-square + X-1 = 0, find the value of X-cube + 2x-square + 3. 4. Factorization factor x-square + 7x-18 =? 5. Common factor of polynomial x-square-4, x-square-7x + 10, x-square-4x + 4? 6. Nuo x-square + 4x + y-6y + 13 = 0, then the values of X and Y are? 7

1. Late return to spend long timid, vast and guanchou
2. It needs to be considered
Because (the one represented by three points) x + 1 = 0, so x + x = 1
Simplify X-cube + 2x-cube + 3
=X (x + x) + 3
Bring in X + x = 1
Original formula = x + 3
4. X square + 7x-18
=(x + 2) (X-9) + 7x is uncertain, right
5.（x+2)
6. X = - 3, y = 2, conjecture and guess, the answer should be right, but the process will not be written

3x(2x-5)+2x(1-3x)=

Original formula = 6x & # 178; - 15x + 2x-6x & # 178;
=-13X