After the image of the function y = 3 / x + A is shifted one unit to the left, the image C1 of y = f (x) is obtained. If the curve C1 is symmetric about the origin, then the value of real number a is

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• 1. Given the function FX = 2sinxcosx-2cos ^ 2x + 1, the image of the function FX is shifted to the right by 6 units to get GX
• 2. The image of the function f (x) = - 2cos (x + π / 4) is shifted a (a > 0) units to the left to get the image of the function y = g (x). If G (x) is an even function, then the image of a is a The minimum value is? Answer in detail, O (∩)_ Thank you
• 3. If the analytic expression of the function y = x ^ 2-4x + 3 is y = x ^ 2, then a =? Process
• 4. When the equation x + y + DX + ey + F = 0 satisfies what condition, it means circle
• 5. The equation x ^ 2 + y ^ 2 + DX + ey + F = 0 is equivalent to the equation of circle A. Sufficient but not necessary condition B, necessary but not sufficient condition C, sufficient and necessary condition D, neither sufficient nor necessary condition
• 6. To make the two intersections of the circle x ^ 2 + y ^ 2 + DX + ey + F = 0 and the X axis on both sides of the origin,
• 7. When d ^ 2 + e ^ 2-4f > 0, the quadratic equation x ^ 2 + y ^ 2 + DX + ey + F > 0 is called the equation of circle Is that right?
• 8. The general equation of high school mathematics circle x ^ 2 + y ^ 2 + DX + ey + F = 0, f must be less than zero? What?
• 9. What is the condition that "d square + e square - 4f > 0" is the equation x square + y square + DX + ey + F representing a circle?
• 10. Excuse me, the general equation of this circle x + y + DX + ey + F = 0, why D + e-4f > 0? How is d + e-4f > 0 obtained?
• 11. If the image of odd function y = f (x) is translated by two units along the positive direction of X axis, the resulting image is C. If C1 and C are symmetric about the origin, then C1 corresponds to the function
• 12. Monotone increasing interval of function y = xcosx SiNx
• 13. Given that f (x) = x, G (x) = RF (x) + SiNx is a decreasing function on the interval [- 1,1] Finding the maximum of R
• 14. Quadratic function y = (2 / 3) x ^ 2 image is above X axis, vertex coordinates (0,0) are origin A0, points A1, A2, A3 , A2008 on the positive half axis of y-axis, points B1, B Quadratic function y = (2 / 3) x ^ 2 image is above X axis, vertex coordinates (0,0) are origin A0, points A1, A2, A3 , A2008 on the positive half axis of y-axis, points B1, B2, B3 If the triangle a0b1a1, a1b2a2, a2b3a3 and a2007b2008a2008 are equilateral triangles, what is the side length of the triangle a2007b2008a2008?
• 15. The image of the quadratic function y = 2 / 3x & # 178; is shown in the figure. The point A0 is at the origin of the coordinate, the points A1, A2, A3... A2010 are on the positive half axis of the Y axis, the points B1, B2, The image of the quadratic function y = 2 / 3x & # 178; is shown in the figure. The point A0 is at the origin of the coordinate, the points A1, A2, A3... A2014 are on the positive half axis of the y-axis, and the points B1, B2, B3,... B2014 are on the image of the quadratic function y = 2 / 3x & # 178; in the first quadrant, △ a0b1a1, △ a1b2a2, △ a2b3a3,... A2013b2014 are equilateral triangles, then the side length of △ a2013b2014 is equal=
• 16. If the square of SiNx + cosx + k = 0 has a solution, then the value range of constant k is small
• 17. The equation SiNx + cosx = a for X is known (1) If the equation has a real solution, find the value range of real number a (2) If the equation has two different real number solutions when x ∈ [0, π], find the value range of real number a and the sum of two real number solutions [- radical 2, + radical 2]; π / 2 The second problem I did was π Please write the detailed process and thinking
• 18. Solution 3 (SiNx) ^ 2-sinxcosx-2 (cosx) ^ 2 = 1
• 19. If x is the minimum internal angle of a triangle, then the maximum value of the function y = SiNx + cosx + sinxcosx is () A. -1B. 2C. −12+2D. 12+2
• 20. Is SiNx = 1 symmetric about the origin? What about cosx = 1? Why?