Given that a, B, C are real numbers, f (x) = AX2 + BX + C, G (x) = ax + B, when - 1 ≤ x ≤ 1 | f (x) | ≤ 1. (1) prove: | C | ≤ 1; (2) prove: when - 1 ≤ x ≤ 1, | g (x) | ≤ 2; (3) let a > 0, when - 1 ≤ x ≤ 1, the maximum value of G (x) is 2, and find f (x)

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• 1. F (x) = log2 [(1-ax) / (x-1)] odd function a is a constant. 1. Find the value of A. 2. Prove that f (x) monotonically decreases in the interval (1, positive infinity), 3.3. If the inequality f (x) B - (1 / 2) ^ x holds for any value of X on [3,5], find the value range of real number B
• 2. How to judge whether a function is even or odd
• 3. What is "odd function. Even function"? We don't have that in our math books, But there are some problems about odd function and even function Please be more specific
• 4. Given that f (x) is an even function, G (x) is an odd function, f (x) + G (x) = x ^ 2 + 2 ^ x, find f (1)
• 5. Let f (x) be a continuous even function on (- ∞, + ∞), and prove that f (x) = ∫ (0 → x) f (T) DT is an odd function
• 6. How to write a function in the form of an odd function and an even function Take F (x) = x + 1 / (2 + x) as an example,
• 7. It is known that the domain of definition of functions f (x) and G (x) is r, where f (x) is odd, G (x) is even, and f (x) + G (x) = 1 / (the square of x-x + 1) Finding the analytic expressions of F (x), G (x)
• 8. It is known that f (x) is an odd function and G (x) is an even function. When x ≥ 0, f (x) = LG (x + 1); when x < 0, G (x) = f (x), the analytic expression of G (x) when x > 0 is obtained
• 9. Given FX = x square + ax + 1, if it is even function, find a
• 10. If the even function f (x) defined on R monotonically decreases on (- ∞, 0], and f (- 1) = 0, then the solution set of inequality f (x) > 0 is () A. （-∞，-1）∪（1，+∞）B. （-∞，-1）∪（0，1）C. （-1，0）∪（0，1）D. （-1，0）∪（1，+∞）
• 11. The relationship between the slope of focus chord and the ratio of focus chord and eccentricity of conic curve? RT
• 12. How to find the locus of the middle point of a line segment whose distance between two points on a conic curve is fixed Take the parabola as an example: Y & # 178; = 2px, (P > 0), a and B are two points on the parabola, and ab = 3, find the trajectory equation of the midpoint m in ab
• 13. The midpoint problem of conic chord To solve the linear equation of the chord of hyperbola with a (m, n) as the midpoint, we can use f (x1) - f (x2) to get the result. But why does it not exist?
• 14. F1, F2 are the two focal points of the ellipse X29 + Y27 = 1, a is the point on the ellipse, and ∠ af1f2 = 45 °, then the area of △ af1f2 is___ ．
• 15. What is the area of the triangle f2ab if a straight line passes through the left focus F1 of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1 and the line parallel to the Y axis intersects the ellipse and ab? There is another problem: the two foci F1F2 of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1, P is the point on the ellipse, if the triangle f1pf2 is a right triangle (angle f1pf2 = 90 degrees), find the area of the triangle f1pf2
• 16. The line L passing through the focus f on the ellipse 2x ^ 2 + y ^ 2 = 2 intersects the ellipse at two points a and B to find the maximum area of Δ AOB (o is the origin) The answer is only √ 2 / 2. Is there anything wrong in it? Or is the answer wrong There's a wrong step in the middle. Oh, forget it
• 17. If the line y = KX intersects the ellipse x ^ 2 / 4 + y ^ 2 = 1 at two points a and B, and ab ≥ √ 10, find the value range of K
• 18. As shown in the figure, the straight line y = kx-1 intersects the x-axis and y-axis at two points B and C respectively, Tan ∠ OCB = 12 (1) Find the coordinates of point B and the value of K; (2) if point a (x, y) is a moving point on the line y = kx-1 in the first quadrant, try to write out the functional relationship between the area s of △ AOB and X when point a moves; (3) explore: under the condition of (2): ① when point a moves to what position, the area of △ AOB is 14; ② if it holds, whether there is a point P on the X axis So that △ POA is an isosceles triangle? If it exists, please write the coordinates of all P points that meet the condition; if not, please explain the reason
• 19. In the plane rectangular coordinate system, the coordinates of point a are (3, - 4), its symmetry about y axis, the coordinates of point B are (), △ OAB are () triangles
• 20. In the plane rectangular coordinate system, B and a are on the X and Y axes respectively, and the coordinate of B is (3,0) ∠ ABO = 30 degree AC bisection ∠ OAB intersects X axis at C (1) Find the coordinates of point C (2) If D is the middle point of AB, ∠ EDF = 60 °, (E on AC, f on BC), it is proved that CE + CF = OC