The graph of function f (x) defined on R has two symmetry axes x = A and x = B (a is not equal to b). Find the period of F (x)

The graph of function f (x) defined on R has two symmetry axes x = A and x = B (a is not equal to b). Find the period of F (x)

Building to do more questions ah, this is the basis of the problem oh

If the function y = f (x) - X has no zero point, for the quadratic function f (x) = ax ^ 2 + BX + C (a ≠ 0),
If the function y = (F, x) - X has no zero point, the following four conclusions are given about the quadratic function f (x) = ax ^ 2 + BX + C (a ≠ 0)
① The function y = f ((FX)) - x must have no zeros. ② the function y = f (f (x)) + X must have no zeros
③ When a > 0, X ∈ R f (f (x)) > x 4, if a + B + C = 0, then a < 0
The correct serial number is________

The correct serial number is_ ①③④
Because the graph of the function f (x) has no intersection with the line y = x,
So f (x) > x (a > 0) or F (x) < x (a < 0) is always true
Because f [f (x)] > F (x) > x or f [f (x)] < f (x) < x is constant,
So f [f (x)] = x has no real root;
Therefore, 1;
If a > 0, then the inequality f [f (x)] > F (x) > x holds for all real numbers X;
Therefore, it is correct;
If a + B + C = 0, then f (1) = 0 < 1, then a < 0,
Therefore, it is correct;

It is known that 2 is the zero point of the function f (x) = ax + B (a is not equal to 0), and the function g (x) = ax ^ 3 + BX ^ 2 + X has an extreme point in the interval (0,1), then the value range of the real number a is the same

After obtaining the relationship between a and B, G (x) is reduced to the form of X (K (x + m) ^ 2 + n), where k, m and N are composed of a and B, then it is easy to get the conclusion according to the extreme value of (0,1)

The known function y = x ^ 3 + 3ax ^ 2 + 3bx + C has an extreme value at x = 2, and the tangent slope at x = 1 in the image is - 3（
Know that the function y = x ^ 3 + 3ax ^ 2 + 3bx + C has an extreme value at x = 2 and the tangent slope at x = 1 is - 3 (1) find the monotone interval of the function (2) find the difference between the maximum and minimum of the function

F & # 39; (x) = 3x & # 178; + 6AX + 3b is obtained from the meaning of the title. F & # 39; (2) = 12 + 12a + 3B = 0 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; F & # 39; (1) = 3 + 6A + 3B = - 3 & nbsp; & nbsp; the solution is a = - 1, B = 0, so f & # 39; (x) = 3x & # 178; - 6x = 3x (X-2), f (x) = x & # 179; -

1. What is the number to the nth power of the number 6? (n is a positive integer)?
2. For the nth power of the number a (n is a positive integer), when a takes one of the 10 numbers from 0 to 9, what are the numbers that are not affected by the exponent n
3. For the power of the number 4N, with the change of the positive integer n, what's the rule of its digits?
4. For the n-th power of a (a takes 0, 1, 2,..., 9, n as positive integers), what else do you find? How do you find it?

1. The n-th power of the number 6? (n is a positive integer) is 6
2. In addition to 6, there are 0, 1, 5

A monomial plus polynomial 9 (x-1) ^ 2 is equal to the square of an integer. Try to find such a monomial, try to find such a monomial

9(x-1)^2
=9x^2-18x+9
9(x+1)^2=9x^2+18x+9
9(x+1)^2-9(x-1)^2=36x
So the monomial is 36x

The following function with no tangent at x = 0 is a y = 3x ^ 2 + cosx b y = xsinx c y = 1 / x + 2x d y = 1 / cosx

The tangent point of tangent should be on the curve, y = 1 / x + 2x has no meaning at x = 0, that is, x = 0 cannot be taken, so there is no tangent at x = 0
Choose C

If (a + b) ² = 25, (a-b) ² = 9, then ab=

（a+b)²=25,（a-b）²=9
（a+b)²-（a-b）²=a²+2ab+b²-a²+2ab-b²=4ab=25-9=16
ab=16/4=4

In the plane rectangular coordinate system, the coordinate of point a is (4,0), point P is on the straight line y = - x + m, and AP = OP = 4. Find the value of M

As shown in the figure, when the point P is in the first quadrant, OM = 2, Op = 4. In RT △ OPM, PM = op2-om2 = 42-22 = 23, (4 points) ∵ P (2, 23) ∵ point P is in y = - x + m, ∵ M = 2 + 23. (6 points) when the point P is in the fourth quadrant, according to the symmetry, p '(2, - 23) ∵ point P' is in the fourth quadrant If y = - x + m, then M is 2 + 23 or 2-23

Solution equation: 3.4x-9.8 = 1.4x + 9

3.4x-9.8=1.4x+9
3.4X-1.4X=9+9.8
2X=18.8
X=9.4