If the function f (x) has f (x) + 2F (- 1 / x) = - 3x for all real numbers with X ≠ 0, find the analytic expression of F (x)

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• 1. The function f (x) = x ^ 3 + ax ^ 2 + BX (a, B are constants) defined on R obtains the extremum at x = - 1. The tangent of the image of F (x) at point P (1, t) is parallel to The function f (x) = x ^ 3 + ax ^ 2 + BX (a, B are constants) defined on R obtains the extremum at x = - 1, and the tangent of the image of F (x) at point P (1, t) is parallel to the straight line y = 8x. (1) find the analytic expression of function f (x); (2) find the maximum and minimum of function f (x)
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• 6. Given the functions f (x) = loga (x) and G (x) = 2loga (2x + T-2), (a > 0, a ≠ 1, t ∈ R), the tangents of the image at x = 2 are parallel to each other (1) Finding the value of T (2) Let f (x) = g (x) - f (x), when x ∈ [1,4], f (x) ≥ 2 is constant, and the value range of a is obtained Note: A is the log base
• 7. If there are two tangent lines perpendicular to each other on the image of function f (x) = ax + SiNx (a is a real number), then the value of a is
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• 9. The first polynomial is 2x & sup2; - 2XY + 3Y, the second one is less than 2 times of the first one by 1, and the third one is multinomial The first polynomial is 2x & sup2; - 2XY + 3Y, the second polynomial is less than 2 times of the first polynomial by 1, and the third polynomial is the sum of the first two polynomials. Find the sum of the three polynomials.
• 10. The polynomial 2x ^ 2 - 2x + 4Y - 2XY - 3Y ^ 2 is written as the difference between quadratic term and primary term
• 11. Y = FX is an odd function defined on R. when x > 0, FX = x + LNX, then the number of real numbers of the equation FX = 0 is
• 12. The odd function f (x) defined on R satisfies: when x > 0, f (x) = 2009 ^ x + log2009 x, then the number of real roots of equation f (x) = 0 is? F (x) = 2009 ^ x + log2009 (x) is there any conversion relationship between 2009 ^ X and log2009 x
• 13. If f (x) is an odd function defined on R with a period of 3 and f (2) = 0, then how many real solutions does the equation f (x) = 0 have in the interval (0,6)
• 14. F (x) and G (x) are functions defined on R, the equation x-f (g (x)) = 0, G (f (x) can not be A X^2+X-1\5 Bx^2+x+1\5 Cx^2-1\5 DX^2+1\5 Let f (x) = x, then G (f (x) = g (x) = f (g (x)) can be obtained I want to ask 1 why we can set f (x) = x, is it because of the equation, I personally think f (x) should not be equal to x, but it is If f (g (x)) = x can be regarded as f (x) = x, and the rule of F is not x, how should we look at it
• 15. If the definition field of function f (x) is {x | x not = 0}, and f (x) - 2F (1 / x) = 3x, then the analytic expression of F (x) is
• 16. If the definition field of function f (x) is {x | x ≠ 0}, and f (x) - 2F (1 / x) = 3x, then the analytic expression of F (x) is___ The parity of F (x) is___
• 17. If the function f (x) defined on R satisfies the relation f (x) + 2F (x / 1) = 3x, then the value of F (2) is? With steps,
• 18. Let f (x) be defined on (- ∞, 0) ∪ (0, + ∞), and f (x) satisfy the relation f (x) + 2F (1 / x) = 3x
• 19. Given that the function f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = - f (x). When x belongs to [0,2], f (x) = 3x + 2, then the analytic expression of the function in the interval [- 4,0] is?
• 20. Let f (x) be an even function defined on R, when x < 0, f (x) = 3x ^ 2-e ^ x, find the analytic expression of F (x) when x > 0!