If the function f (x) = 2ax2-x-1 has exactly one zero point in (0,1), then the value range of a is () A. (1,+∞)B. (-∞,-1)C. (-1,1)D. [0,1)
When △ = 0, a = - 18, there is a zero point x = - 2, which is not on (0, 1), so it does not hold. The function f (x) = 2ax2-x-1 has exactly a zero point in (0, 1), that is, f (0) f (1) < 0, that is - 1 × (2a-1) < 0. The solution is a > 1, so a is selected
RELATED INFORMATIONS
- 1. (related functions) Given the set a = {Y / y = x Square-1, X contained in R}, B = {X / y = root 2X-4}, then the intersection of a and B = -, the union of a and B=—— The result is {X / X is greater than or equal to 2}, and the next lattice is {X / X is greater than or equal to - 1}
- 2. Given the function f (x) = 2Sin - (2x - π / 6), 1. Write the equation of symmetry axis, symmetry center and monotone interval of function f (x). 2. Find the maximum and minimum value of function f (x) in the interval [0, π / 2]
- 3. f(x)=x/(x^2+1) Does the equation f (x) - (x-1) / x = 0 have a root? If there is a root x0, ask for an interval (a, b) of length 1 / 4, so that XO ∈ (a, b). If not, explain the reason?
- 4. It is known that y = 2Sin (Wx + a-pai / 6) 0
- 5. The known function f (x) = 2Sin (Wx + φ) (W > 0, - π / 2)
- 6. Given that the function y = 2Sin (Wx + Fei) is an even function (w > 0,0 < Fei < π), the distance between two adjacent symmetry axes of an image is π 2, and f (π 9) is obtained After the image of the function is shifted to the right by π - 6 units, the decreasing interval of the function is obtained
- 7. Known w > 0,0
- 8. It is known that ω > 0,0
- 9. Given the function f (x) = sin (Wx + π / 4), where w > 0, if the distance between two adjacent symmetrical axes of the function f (x) image is equal to π / 3, the analytic expression of the function is obtained And find the minimum positive real number m so that the function corresponding to m unit length of the function image is even
- 10. If the image of functions g (x) and f (x) = - 2x + 1 is symmetric with respect to y = x, then G (x)=___ Ask for detailed explanation
- 11. Given that the function g (x) = - x2-3, f (x) is a quadratic function, when x ∈ [- 1,2], the minimum value of F (x) is 1, and f (x) + G (x) is an odd function, the analytic expression of F (x) is obtained
- 12. The formula of function image symmetry and periodic function 1. On the symmetric function, what I want to ask is f|x + a|, which is about x =? What about symmetry? I remember symmetry seems to have a formula, I can't remember. 2. F (x) = loga | x + 1 | this function is symmetric with respect to x = - 1. I drew it with images. But how to express it in function? Is f (x + 1) = f (- x-1)? 3. I'd like to know about periodic functions. F (x + a) = f (x-a) is this a periodic function? What is the cycle? There seems to be a formula for periodic function. Find that formula. 4. Can f (x) = f (x + 1) deduce f (x + 1) = f (x + 2)? =============== Every question is ten. >
- 13. In the following functions, the minimum positive period is π, and the image is symmetric with respect to the line x = π / 3 Why is the answer not y = sin (2x + π / 6) Is the axis of symmetry of SiNx K π + π / 2? Is moving to the left symmetrical about the straight line x = π / 3? Shouldn't adding left and subtracting right be adding π / 6? Why is the answer subtracting
- 14. In the following functions, the period is π, and the symmetric function of the image with respect to the line x = π / 3 is () A.y=2sin(x/2+π/3) B.y=2sin(x/2-π/3) C.y=2sin(2x+π/6) D.y=2sin(2x-π/3) The answer is to exclude AB with the definition first, the period is π, AB does not hold Then, x = π / 3 is the axis of symmetry, From term C, we can take the symmetric point (2 π / 3, - 1 / 2) of point (0, - 1 / 2) with respect to x = π / 3, and substitute x = 2 π / 3 into term C, then y = - 2 ≠ - 1 / 2 doubt! Q: Why shouldn't y = - 1 when x = 0 in the C-term (0, - 1 / 2)?
- 15. In the following functions, where the minimum positive period is π and the image is axisymmetric with respect to the line x = π 3 () A. y=sin(2x-π3)B. y=sin(2x+π6)C. y=sin(2x-π6)D. y=sin(12x+π6)
- 16. Given the function y = - x ^ 2 + | x + 2, seek the image, seek the monotone interval, seek the maximum value of the function
- 17. Given the function y = (1 / 2) ^ | x + 2 | (1), make its image; (2) point out its monotone interval; (3) when determining the value of X, y has the maximum value
- 18. Let f (x) = (sinwx + coswx) ^ 2 + 2cos ^ 2wx (W > 0) have a minimum positive period of 2 π / 3 Finding the minimum positive period of W
- 19. Given the vector a = (m, n), B = (coswx, sinwx), where m, N, W are constants, and W > 0, X ∈ R, the function y = f (x) = vector a * and the period of vector B is π. When x = π, 12, the maximum value of the function is 1 (1) Finding the analytic expression of function f (x) (2) Write the axis of symmetry of y = f (x) and prove it
- 20. Let the minimum period of function f (x) = (sinwx + coswx) ^ + 2cos ^ Wx (W > 0) be 2 / 3, and find the value of W