When n is a positive integer, the function n (n) represents the largest odd factor of n When n is a positive integer, the function n (n) represents the largest odd factor of N, such as n (3) = 3, n (10) = 5, Let Sn = n (1) + n (2) + n (3) + n (4) +... + n (the nth power of 2) + n (the nth power of 2) The answer is (n power of 4 + 2) / 3,

The solution process is also very simple. You can know that the largest odd factor of odd number is due to itself. This is an invariable truth. It is based on this consideration that Sn can be reorganized once. Of course, recombination is recombination! Sn = n (1) + n (2) + n (3) + n (4) +... + n (2's nth power - 1) + n (2's nth power) = n (1)

How to calculate the domain of definition f (x) = ㏑ (1-x) -㏑ (1 x), judge the parity of function and prove it

1. Domain
1-x > 0 and 1 + x > 0
x－1
－1

Find the coordinates of the intersection point of the function y which is equal to negative x plus 5 and the function y which is equal to 2x minus 1

(2,3) you are a student of grade one!

The abscissa of the intersection point P between the image of a linear function and the line y = 2x + 1 is 2, and the ordinate of the intersection point Q between the image of a linear function and the line y = x + 2 is 1
If the intersection of this function image with x-axis and y-axis is a and B respectively, calculate the area of △ OAB

According to the meaning of the question, we can find that the coordinates of P point are (2,5) and Q point are (- 1,1)
This function passes through two points P and Q, let the equation be y = ax + B, substitute two points PQ, and get a = 4 / 3, B = 7 / 3
That is, the equation y = 4 / 3 * x + 7 / 3 intersects with X axis at (- 7 / 4,0) and Y axis at (0,7 / 3)
So triangle area = (7 / 4) * (7 / 3) * (1 / 2) = 49 / 24

If the image of the function y = loga (2x + 1 of x-1) passes through the fixed point P, what is the coordinate of the point P

Because the logarithm function y = loga (x) passes through the point (1,0)
Let (2x + 1) / (x-1) = 1, y = 0
(2x + 1) / (x-1) = 1, the solution is x = - 2
So the function y = loga ((2x + 1) / (x-1)) passes through the fixed point (- 2,0)

If the image of function y = loga (x + 2) (a > 0, a ≠ 1) passes through the fixed point P, then the coordinates of point P are______ ．

When x = - 1, y = 0, the coordinate of point P is p (- 1,0)

Given that the function f (x) = x2-2ax + A has the minimum value in the interval (- ∞, 1), then the function f (x) / X ()
A. There are two zeros B. there is a zero C. There is no zero D. It is impossible to determine

D. It can have a zero or no zero,

The function f (x) = - x2 + 2aX + 1-A has the maximum value 2 in the interval [0,1]. Find the value of real number a

Symmetry axis X = a, when a < 0, [0,1] is the decreasing interval of F (x), f (x) max = f (0) = 1-A = 2 ∥ a = - 1; when a > 1, [0,1] is the increasing interval of F (x), f (x) max = f (1) = a = 2 ∥ a = 2; when 0 ≤ a ≤ 1, f (x) max = f (a) = a2-a + 1 = 2, the solution is a = 1 ± 52, which is contradictory to 0 ≤ a ≤ 1; so a = - 1 or a = 2

Finding the minimum value of the function f (x) = x ^ 2-2ax + 1 in the interval [0,2]

f(x)=(x-a)^2+1-a^2
The axis of symmetry is x = a
If the axis of symmetry is in the interval [0,2], then 0=

The square of F (x) = - x + 2aX is a decreasing function in the interval [1,2], and the value range of a is obtained
I'm taking both 1 and 2 in to calculate that - 1 / 2 is less than or equal to a and less than or equal to 1. But analytically, the function is a decreasing function on the right side of the symmetry axis X = a, so a is less than or equal to 1. Why?

If the parabola opening of F (x) image is downward, the function is a decreasing function on the right side of its axis of symmetry x = - A / 2,
a