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If the function f (x) defined on R is symmetric about x = A and about point (B, 0), and a is not equal to B, the period of function f (x) is obtained
2 Ib-aI
The graph of the function f (x) defined on R is symmetric with respect to points a (a, b), B (C, b) (where C is not equal to a), and the period of F (x) is calculated?
T=2|a-c|
T=|a-c|
1. The general term formula of sequence an is an = n + B / N. if an ≥ A5 for any n ∈ n *, then the value range of real number B is?
2. The image of the odd function f (x) with the domain R is symmetric with respect to the line x = 1. When x belongs to [0.1], f (x) = x and the equation f (x) = log2013x (2013 is the subscript), the number of real roots is a.1006 b.1007 c.2012 d.2014
3. Given that the image of function f (x) is symmetric about point a (0,1) with respect to h (x) = x + 1 / x + 2, find the analytic expression of F (x)
First of all, the value of B must be positive, because when B is negative, the minimum value of an should be obtained at n = 1, so it is contradictory to the meaning of the topic, so it is directly A5
Find the unknown x (30-x) 2 + 4x = 84
x=12
It is known that the definition field of function f (x) is constant on R and satisfies the following conditions: F (x2-x1) = f (x2) - f (x1) + 1, f (x) - 1, f (x) + 1
0&2
Which of the functions y = sin2x and y = cos2x is a decreasing function on (π / 2, π)
Please explain the process
y=cos2x
It is suggested that you draw directly for easy understanding
If the length of one side of the rectangle is root 7 and the length of the diagonal is 4, the area of the shape is known
Let the other side be X. from the Pythagorean theorem, we get that,
x²+(√7)²=4²
The solution is x = 3
So the area of the rectangle is √ 7x = 3 √ 7
Known: x 2 + XY + y = 14, y 2 + XY + x = 28, find the value of X + y
∵ x2 + XY + y = 14 (1), Y2 + XY + x = 28 (2), ∵ ① + 2, we get: x2 + 2XY + Y2 + X + y = 42, ∵ (x + y) 2 + (x + y) - 42 = 0, ∵ (x + y + 7) (x + y-6) = 0, ∵ x + y + 7 = 0 or x + y-6 = 0, the solution is: x + y = - 7 or x + y = 6
19 * (2x + 5.2) = 201.4
19*(2x+5.2)=201.4
2x+5.2=201.4/19=10.6
2x=10.6-5.2=5.4
x=2.7
If the slopes of the straight lines of the inscribed parallelogram ABCD of ellipse X & # 178 / 16 + Y & # 178 / 9 = 1 all exist, then the product of the slopes of the straight lines AB and CD is?
Special value method
Taking the four vertices of the ellipse as the four vertices of the parallelogram just meets the meaning of the problem
A(-4,0),B(0,-3),C(4,0),D(0,3)
K(AB)=-3/4,K(CD)=-3/4
So the product of the slope of line AB and CD is 9 / 16
RELATED INFORMATIONS
- 1. 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)
- 2. Given the function f (x) = x + m / x, and the function image passes through the point (1,5), judge the monotonicity of function f (x) on [2, + ∞), and prove your conclusion with the definition
- 3. Judge and prove the monotonicity of function f (x) = X-1 / x + 2 on (2, positive infinity), and draw its general image
- 4. We know that the function f (x) = 2x ^ 2 + x-k, G (x) = ax ^ 3 + BX ^ 2 + CX + D (a is not equal to 0) is an odd function on R. when x = 1, G (x) obtains the extremum - 2 (1) finds the monotone interval and the maximum of the function; (2) if f (x) is less than or equal to (x) for any closed interval from - 1 to 3, finds the range of real number K 2) If f (x) is less than or equal to G (x) for any closed interval where x belongs to - 1 to 3, find the range of real number K
- 5. 1. The function y = ax ^ 2 + BX + C (a is not equal to 0) is a necessary and sufficient condition for an image to cross the origin_ 2. Known proposition p: "inverse ax belongs to R, inverse EM belongs to R, so that 4 ^ X-2 1. The function y = ax ^ 2 + BX + C (a is not equal to 0) is a necessary and sufficient condition for an image to cross the origin 2. Given proposition p: "inverted ax belongs to R, inverted EM belongs to R, so that 4 ^ X-2 ^ (x + 1) + M = 0", if proposition p is a false proposition, then the value range of real number m is
- 6. If the function f (x) = ax + 2 (a > 0 and a is not equal to 1) passes through a (2,6), then f (3) =?
- 7. It is known that the function f (x) = the cube of X + the square of AX + 3bx + C (B is not equal to 0), and G (x) = f (x) - 2 is an odd function?
- 8. If f (x + 1) = x & # 178; - 2x-15, then f (16) =?
- 9. ① Given f (2x) = 2x + 3, find f (x) 2. Given g (x) = 1-2x, f [g (x)] = 1-x & # 178; / X & # 178;, find the value of F (1 / 2)
- 10. Given that X and y satisfy X & # 178; + Y & # 178; + 5 / 4 = x-2y, what is the value of 2x + y?
- 11. Try to discuss the number of zeros of function H (x) = f (x + 1) - G (x) in the interval (- 2,0) Given function f (x) = LG (x + 1) 1. If G (x) is an even function and G (x) = g (x + 2), when 0 ≤ x ≤ 1, G (x) = f (x), find the analytic expression of y = g (x) (x belongs to [- 2,0]; 2. Under the condition of (1), the number of zeros of the function H (x) = f (x + 1) - G (x) in the interval (- 2,0) is discussed
- 12. The zero point of function y = (AX-1) (X-2) is discussed
- 13. If y = f (x) satisfies f (a) · f (b) < 0 on [a, b], then y = f (x) has zero in (a, b) This sentence is wrong, but I want to know what is wrong
- 14. Given that a, B and C belong to R, the function f (x) = ax ^ 3 + BX ^ 2 + CX satisfies f (1) = 0 Let the derivative of F (x) be f '(x), and f' (0) * f '(1) > 0 Finding the range of C / A
- 15. The function f (x) = ax ^ 3 + BX ^ 2 + CX + 3 defined on R satisfies the following conditions 1. F (x) is a decreasing function on (0,1) and an increasing function on (1, + OO) 2. F '(x) is even function 3. The tangent of F (x) at x = 0 is perpendicular to the line y = x + 2 Finding the analytic expression of function y = f (x) Let g (x) = 4lnx-m, if x belongs to [1, e], Let g (x)
- 16. F (x) = x ^ 3 + BX ^ 2 + CX + D (x belongs to R). It is known that f (x) = f (x) - f '(x) is an odd function and f (1) = t (T)
- 17. We know that the function is an odd function on f (x) = AX3 + CX + D. when x = 1, we take the extremum - 2 and find the monotone interval and maximum of F (x)
- 18. For the function f (x), if there exists x0 ∈ r such that f (x0) = x0 holds, then x0 is called the fixed point of F (x). It is known that f (x) = AX2 + (B + 1) x + (B-1) (a ≠ 0) (1) When a = 1, B = - 2, find the fixed point of F (x)
- 19. For the function f (x), if there exists x0 ∈ r such that f (x0) = x0 holds, then x0 is called the fixed point of F (x). It is known that the two fixed points of F (x) = AX2 + (B-7) x + 18 are - 3 and 2 respectively: (I) finding the value of a, B and the expression of F (x); (II) finding the value range of F (x) when the domain of F (x) is [0,1]
- 20. If the x power of function FX = (x power of 4-b) / 2 is odd, then B=