Let f (x) be defined on (- ∞, 0) ∪ (0, + ∞), and f (x) satisfy the relation f (x) + 2F (1 / x) = 3x

RELATED INFORMATIONS

• 1. 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,
• 2. 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___
• 3. 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
• 4. 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
• 5. 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)
• 6. 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
• 7. 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
• 8. 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)
• 9. 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)
• 10. The tangent equation of curve y = INX at point (E, f (E)) is
• 11. 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?
• 12. 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!
• 13. It is known that the function f (x) is an even function defined on R. when x is greater than 0, f (x) = x * x + 3x-1, the analytic expression of F (x) is obtained
• 14. It is known that f (x) is an even function defined on R, and for any x belonging to R, f (x + 2) = f (X-2). When x belongs to [0,2], f (x) = 3x + 2, find the analytic expression of F (x) on [4,0]
• 15. (1 / 2) it is known that f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = f (2-x). When x belongs to [0,2], f (x) = 3x + 2 (1 / 2) it is known that f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = f (2-x). When x belongs to [0,2], f (x) = 3x + 2, find f (x)
• 16. Given the function f (x) = lg1-x / 1 + X, 1. Find the definition domain of the function 2. The value range of X that makes f (x) > 0 Let f (x) = 1-2 to the power of X + 2 / 1, find the range of function value
• 17. Given that y = f (x) is a decreasing function in the domain (- 1,1), and f (1-A) < f (3a-1), then the value range of a is
• 18. If f (x) is an increasing function in the domain [- 1.1], and f (X-2) > F (1-x), then the value range of X is
• 19. Given that f (x) = 1 / root x 2 + ax + A-1 is defined as (- ∞, 1-A) ∪ (- 1, + ∞), the value range of a is obtained
• 20. If the domain of function f (x + 1) is [0,1], then the domain of function f (3x-1) is [0,1]______ ．