Given that the function f (x) = ax ^ 2 + BX + C / X is odd in the domain of definition, and f (1) = 2, f (1 / 2) = 5 / 2, what is the analytic expression of the function? Don't calculate the analytic formula. I can do it. Help me prove that f (x) is an increasing function on [1, positive infinity] by definition. Solve the inequality f (T & # 178; + 1) + F (- 3 + 3t-2t & # 178;) < 0. Hurry up. Thank you

Given that the function f (x) = ax ^ 2 + BX + C / X is odd in the domain of definition, and f (1) = 2, f (1 / 2) = 5 / 2, what is the analytic expression of the function? Don't calculate the analytic formula. I can do it. Help me prove that f (x) is an increasing function on [1, positive infinity] by definition. Solve the inequality f (T & # 178; + 1) + F (- 3 + 3t-2t & # 178;) < 0. Hurry up. Thank you

F (1) = a + B + C = 2 ① f (1 / 2) = 25 / 4A + B / 2 + 2C = 5 / 2 ② because f (x) is an odd function in the domain of definition, f (- 1) = - f (1) = a-b-c = - 2 ③ the simultaneous solution is: a = 0, B = 1, C = 1, so the analytic expression of F (x) is: F (x) = x + 1 / X. f (x) is a standard double hook function, and the minimum value on (0. + ∞) is 1

If f (x) = x ^ 2-2x-3, then the number of zeros of F [f (x)] is zero
Why four -=

The equation is reduced to: F (x) = (x-3) (x + 1), so f [f (x)] = (x ^ 2-2x-6) (x ^ 2-2x-2) = (x-1 + (7) ^ (1 / 2)) (x-1 - (7) ^ (1 / 2)) (x-1 + (2) ^ 1 / 2) (x-1 - (3) ^ (1 / 2))
F (1 - (7) ^ (1 / 2)) = f (1 + (7) ^ (1 / 2)) = f (1 - (2) ^ 1 / 2)) = f (1 + (2) ^ 1 / 2)) = 0

The maximum value of function y = - 10sin (2x + π / 6) + 5_____ .
Give me the idea to solve the problem.

When sin (2x + π / 6) = - 1, - 10sin (2x + π / 6) is the largest
ymax=－10*(-1)+5=15

The function y = x ^ 2-2x (0 ≤ x ≤ 3) has both maximum and minimum values, which are () ()

y=(x-1)^2-1
When x = 1, the minimum is y = - 1
When x = 3, the maximum is y = 3

"If a set contains n elements, then the subset of the set is 2n"

2 to the nth power, not 2 * n

For a set of n positive integers, the sum of subset elements is different from each other, and the minimum value of the maximum number is K (n)
It is easy to have K (1) = 1, K (2) = 2, K (3) = 4, K (4) = 7, K (5) = 13
In order to prove that K (6) > = 21, K (7) > = 38, it is better to find 24, 44
What is the conclusion about K (n)?

Hope to give the proof that K (6) = 24, and then give points, thank you!

Find the number of elements in the set M = {m, M = 2N-1, n belongs to n *, and m < 60}, and find the sum of these elements?

2n-1=m

Set of all positive integers less than 6?

There are five kinds of sets with only one element in the set of all positive integers less than 6. Only two elements in the set of {1} {2} {3} {4} {5} have C52 = 10 kinds, only three elements in the set have C53 = 10 kinds, only four elements in the set have C54 = 5 kinds, and five elements in the set have 1 kind

A set of positive integral multiples of 5

5 = {x | x = 5K, K ∈ n, k > 0};
The set of all acute triangles = {x | x is an acute triangle} = {acute triangle}

Let the set a be composed of the positive integers less than 100 divided by 5, then the sum of all the elements is ()
Let the set a be composed of the positive integers less than 100 divided by 5, then the sum of all the elements is ()

5*（1+2+3+…… +20）=1050