Given that function f (x) is an odd function defined on R, f (1) = 0, XF '(x) - f (x) > 0 (x > 0), then the solution set of inequality f (x) > 0 is

Given that function f (x) is an odd function defined on R, f (1) = 0, XF '(x) - f (x) > 0 (x > 0), then the solution set of inequality f (x) > 0 is

If x f '(x) - f (x) > 0, i.e. (XF (x))' > 0, the function y = f (x) / X is an increasing function on x > 0. If y = x is an increasing function on x > 0, then the function y = f (x) = (f (x) / x) * x is an increasing function on x > 0. If f (1) = 0, then f (x) > 0, i.e. f (x) > F (1), x > 1
The solution of the square of X + X + 3 ≥ 0
Let X & # 178; + X + 3 = 0
Δ=1-12=-11＜0
The equation has no solution
There is no intersection with X axis
The solution set of the inequality is (- ∞, + ∞)
The discriminant: △ = 1-120. The opening is upward, so the parabola f (x) is above the x-axis, and f (x) > = 0 holds. So the inequality solution is r
This is very easy to understand. To find a quadratic equation inequality is to draw a parabola, which is the key to find its two intersections with the x-axis. Because your a > 0, the answer is x ≤ (a smaller intersection with the x-axis) or ≥ the other intersection with the x-axis. I'll show you later. If there is no intersection between this graph and the x-axis, all values are greater than 0, so x ∈ r... expand
This is very easy to understand. To find a quadratic equation inequality is to draw a parabola, which is the key to find its two intersections with the X axis. Because your a is greater than 0, the answer is x ≤ (a smaller intersection with the X axis) or ≥ the other intersection with the X axis. I'll show you later. If there is no intersection between this graph and the X axis, all the values are greater than 0 So x ∈ R is folded
The solution of the square of X + X + 3 ≥ 0
△ =1 - 12 < 0
So it must be > 0
The solution of square + X + 3 ≥ 0 of X is x ∈ R
A mathematical problem of quadratic equation of two variables,
A. The distance between the two places is 3km. A starts from a and walks to B. B starts from B and walks to a. the two start at the same time. After 20 minutes, they meet. Half an hour later, the remaining distance of a is twice that of B. the speed of a and B is calculated
Let the speed of a and B be a and B km / h respectively
Meet in 20 minutes (a + b) / 3 = 3
Half an hour later, the remaining distance of institute a is twice that of institute B. 3-A / 2 = 2 (3-B / 2)
a=4 b=5
The speed of a and B is 4 km / h and 5 km / h respectively
Given that the function f (x) is an odd function defined on R, if x > 0, f (x) = 1-2 ^ (- x), then the inequality f (x)
When x = 0, f (0) = f (- 0) = - f (0), f (0) = 0
When x
How to solve math problem 5x (x 0.8) = 22.5
The title should be 5x times 0.8 = 22.5
5x(x 0.8)=22.5
5x=22.5/0.8
5x=28.125
x=28.125/5
x=5.625
Can you tell me which is the multiplication sign and which is the unknown x
5X(5.625X0.8)=22.5
5 times (x-0.8) = 22.5
5 times (x-0.8) divided by 5 = 22.5 divided by 5
x-0.8+0.8=4.5+0.8
x=5.3
A mathematical problem, a quadratic equation of two variables
There are two kinds of freight cars, two big cars and three small cars, which can carry 15.5t goods at a time, five big cars and six small cars can carry 35t goods at a time, and three big cars and five small cars can carry 35t goods at a time
Let the cart transport x T and the trolley transport y t
2X+3Y＝15.5..（1）
5X+6Y＝35.（2）
(2) Formula (1) formula * 2: x = 4
By substituting (1), y = 2.5
So 3x + 5Y = 3 * 4 + 5 * 2.5 = 24.5
Set a big car to transport x tons each time, and a small car to transport y tons each time
2X + 3Y = 15.5, 4x + 6y = 31
5X+6Y=35
X = 4, y = 2.5
Three big cars and five small cars can transport 12 + 12.5 = 24.5 (tons) at a time
Hope to help you
2X+3Y=15.5
5X+6Y=35
The solution is x = 4, y = 2.5
So 3x + 5Y = 12 + 12.5 = 24.5t
The trolley transports XT at one time and the cart transports YT at one time
3x+2y=15.5
6x+5y=35
x=2.5 y=4
5x+3y=24.5
3 carts and 5 carts can transport 24.5t at a time
Given that the function f (x) is an odd function defined on R, when x > 0, f (x) = 1-2-x, then the solution set of the inequality f (x) < - 12 is ()
A. （-∞，-1）B. （-∞，-1]C. （1，+∞）D. [1，+∞）
When x ＞ 0, 1-2-x = 1-12x ＞ 0 is not consistent with the meaning of the title. When x ＜ 0, - x ＞ 0, ∵ f (- x) = 1-2x, and ∵ f (x) is an odd function on R, ∵ f (- x) = - f (x), ∵ f (x) = 1-2x, ∵ f (x) = 2x-1 ＜ - 12, ∵ 2x ＜ 12, ∵ x ＜ - 1, ∵ the solution set of inequality f (x) ＜ - 12 is (- ∞, - 1). So the answer is a
(1) If a ＜ B, then the solution set of X ＞ a, X ＜ B is (). (2) the solution set of inequality system X ＞ - 5, X ＜ 3, X ＞ - 1 is ()
Right now,
1：x∈（a,b）
2：x∈（-1,3）
Mathematical problems of linear equations of two variables
In order to reward the students in the interest group, Mr. Zhang spent 92 yuan to buy two kinds of books: "intellectual challenge" and "interesting math problems". It is known that "intellectual challenge" costs 18 yuan per book, and "interesting math problems" costs 8 yuan per book. How many books did "interesting math problems" buy?
"Intellectual challenge" and "mathematics interesting questions" are a and B books respectively
18a+8b=92
9A + 4B = 46 A, B are integers
So a = 2, B = 7
I bought seven copies of interesting math problems
Given that the domain of F (2x-1) is [- 1,1], find the domain of F (1-3x)
x∈[-1,1)
Then 2x-1 ∈ [- 3,1)
So the domain of function f (1-3x) should satisfy
1-3x ∈ [-3,1)
That is, X ∈ (0,4 / 3]