Let the function FX = x + A / x + B (a > b > 0), find the monotone interval of F (x), and prove the increasing of F (x) in its monotone interval Sex

f(x)=(x+b-b+a)/(x+b)
=1+(a-b)/(x+b)
Because A-B > 0, when x > - B or X-B, or X

RELATED INFORMATIONS

1. Draw the graph of function f (x) = | x ^ 2 + X-2 | and write the monotone interval
2. What is the relationship between derivative function and monotonicity of function? What is the relationship between derivative function and monotonicity of function? How to draw function image by derivative function, or draw derivative function by function? Please give specific examples. Is there a better way to remember them?
3. How to find the symmetry axis, monotonicity and parity of trigonometric functions?
4. Let y = f (x) be an odd function on the domain R, and f (X-2) = - f (x) holds for all x belonging to R, then the symmetry axis of F (x) image?
5. If the function defined on R, y = f (x), and the image of y = f (x + 2) is symmetric with respect to x = 0, then the symmetry axis of the image of the function y = f (x)
6. Given the function f (x) = log, take a as the base 1 + X / 1-x (a > 0, a ≠ 1) to find the inverse function
7. The inverse function of function f (x) log with base 2 (x + 1) (x > = 0) is f ^ - 1 (x)=
8. If the inverse function of function f (x) is f ^ (- 1) (x) = log with 2 as the base x, then f (x)=
9. The inverse function f ^ - 1 (x) = () of function f (x) = log (2) (1 + 1 / x) (x > 0)
10. The monotone increasing interval of function f (x) = log5 (2x + 1) is______ ．
11. F (x) = x2 + 4x + 3, t ∈ R, the function g (T) represents the minimum value of function f (x) in the interval [T, t + 1], and the expression of G (T) is obtained
12. The minimum value of the function f (x) = x2-4x-4 in the closed interval [T, t + 1] (t ∈ R) is denoted as G (T). (1) try to write the functional expression of G (T). (2) make the image of G (T) and find the minimum value of G (T)
13. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
14. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
15. FX = x ^ 2-2x + 2, X ∈ [T, t + 1], t ∈ R, find the expression of the minimum value g (T) of function FX
16. Let f (x) = x ^ 2-2x + 2, let the minimum value of F (x) on [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
17. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
18. Let the minimum value of F (x) = x2-4x-4 on [T, t + 1] (t belongs to R) be g (T). Write out the functional expression of G (T)
19. Given that the minimum value of the function f (x) = x ^ 2-4x + 2 in the interval [T, T-2] is g (T), find the expression of G (T)
20. As shown in the figure, the image of the quadratic function y = 1 / 2x-x + C intersects with the X axis at two points a and B respectively. The symmetric point of vertex m about the X axis is m ' February 21, 2013 | sharing As shown in the figure, the image of the quadratic function y = 1 / 2x-x + C intersects with the X axis at two points a and B respectively. The symmetric point of vertex m about the X axis is m ' (1) If a (- 4,0), find the relation of quadratic function; (2) Under the condition of (1), calculate the area of the quadrilateral ambm '; (3) Is there a parabola y = 1 / 2x-x + C, so that the quadrilateral ambm 'is a square? If it exists, ask for the functional relation of the first parabola; if not, please explain the reason