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

When x > 0, f (x) = x + LNX is an increasing function, and f (1 / E) = 1 / E - 10, so f (x) has a unique zero point on (0, + ∞), and the zero point is in (1 / E, 1). Because f (x) is an odd function, the image is symmetric about the origin, so f (x) also has a unique zero point on (- ∞, 0)

RELATED INFORMATIONS

1. 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)
2. 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)
3. The tangent equation of curve y = INX at point (E, f (E)) is
4. Given the function y = f (x) = x2 + 3x + 2aX, X ∈ [2, + ∞); (1) when a = 12, find the minimum value of function f (x); (2) if f (x) > 0 holds for any x ∈ [2, + ∞), find the value range of real number a
5. Tangent equation () A. y=x-1B. y=3x-3C. y=-x-1D. y=3x+1
6. If the derivative of the function f (x) = SiNx / X is f '(x), then f' π=
7. 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
8. 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
9. (2x^3y)^2×(-2xy)+(-2x^3y)^3÷(2x^2)
10. 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.
11. 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
12. 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)
13. 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
14. 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
15. 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___
16. 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,
17. Let f (x) be defined on (- ∞, 0) ∪ (0, + ∞), and f (x) satisfy the relation f (x) + 2F (1 / x) = 3x
18. 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?
19. 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!
20. 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