What is the value of X? 1. Square of root X; 2. Root x-4; 3. Root x + 1 + root 1-x; 4. Root X-1 of x-3

What is the value of X? 1. Square of root X; 2. Root x-4; 3. Root x + 1 + root 1-x; 4. Root X-1 of x-3

1. X is any real number
2、x-4≥0
x≥4
3. X + 1 ≥ 0 and 1-x ≥ 0
X ≥ - 1 and X ≤ 1
So - 1 ≤ x ≤ 1
4. X-1 ≥ 0 and x-3 is not equal to 0
X ≥ 1 and X ≠ 3

Define the operation a * B, if a ≤ B equals a, if a > b equals B, for example, 1 * 2 = 1, then the function f (x) = x ^ 2 * (1 - x)
The maximum value of is

F (x) = x & sup2; * (1 - x)
The key lies in the size of X & sup2; and 1 - X,
If X & sup2; > 1 - x,
X & sup2; + x > 1
If x > 0, then
If X & sup2; + X-1 > 0, we get x > (radical 5-1) / 2
Let X

Define the operation a * b = {a (a is less than or equal to b), B (a is greater than B)}. Then the analytic expression of function f (x) = 1 * x is

According to the defined operation rules:
f（x）=1*x
When x < 1, f (x) = x;
When x ≥ 1, f (x) = 1
That is, f (x) is a piecewise function

Solution equation: x + 14-5x = 1.2

x+14-5x=1.2
14-4x=1.2
14-1.2=4x
12.8=4x
x=3.2

When a line with a slope of 1 intersects an ellipse x ^ 2 / 4 + y ^ 2 / 2 = 1 at two points a and B, and the OAB area of the triangle is the largest, the linear equation is

Let the linear equation be y = x + B ①
We simplify ① into x ^ 2 / 4 + y ^ 2 / 2 = 1
3x＾2+4bx+2b＾2-4=0
In order to make the straight line intersect the ellipse △ > 0, calculate:

(1) In turn, what rules do you find for the number of digits to the nth power of (- 3) (n is a positive integer)? (2) find the number of digits to the 57th power of (- 3)
（-3)¹=-3 （-3)²=9 （-3)³=-27 （-3)⁴=81
The fifth power of (- 3) = the sixth power of - 243 (- 3) = the seventh power of 729 (- 3) = the eighth power of - 2187 (- 3) = 6561
.

Cycle according to the cycle of 3 9 7 1
57 / 4 = 14.1, so the single digit of (- 3) is 3

If n satisfies (n-2012) ^ 2 + (2014-n) ^ 2 = 1, then (2014-n) (n-2012)=________
Such as the title

It should be 3 / 2
Construct a complete square to get the answer
The original formula = = > - 2 (2014-n) (n-2012) + (n-2012 + 2014-n) ^ 2 = 1
====>-2(2014-n)(n-2012)+4=1
=====>(2014-n)(n-2012)=3/2

If the images of functions f (x) and G (x) = () are symmetric with respect to y = x, what is the monotone increasing interval of function y = f (x)?
If the image of functions f (x) and G (x) = (1 / 2) & # 710; X is symmetric with respect to y = x, then what is the monotone increasing interval of function y = f - & sup1; (x)?

Since it is symmetric about y = x, then f (x) = g-1 (x), or G (x) = F-1 (x), so y = F-1 (x) = g (x) = (1 / 2) & # 710; X
And G (x) = (1 / 2) &# 710; X is monotonically decreasing in X ε (- ∞, + ∞)

Calculation: (1) - 32 + 5 × (- 85) - (- 4) 2 ÷ (- 8) (2) (- 3) 2004 × (- 13) 2005 (3) (12 + 13 +) +12005）（1+12+13+… +12004）-（1+12+… +12005）（12+13+… +12004）

(1) The original formula = - 9-5 × 85-16 △ (- 8) = - 9-8 + 2 = - 15; (2) the original formula = (- 3) 2004 × (- 13) 2004 × (- 13) = [(- 3) × (- 13)] 2004 × (- 13) = 12004 × (- 13) = - 13; (3) let 12 + 13 + +12005=a，12+13+… +12004 = B, then the original formula = a (1 + b) - (1 + a) · B = a + ab-b-ab = A-B = 12005

Given that the coordinate of point P is (- 4,3), we can get point P1 by symmetric transformation of point P about X axis, and then we can get point P2 by translation transformation of P1 8 units to the right
The distance between P and P2 is 10. Do you think that's right? Why

P1 is (- 4, - 3)
Then P2 is (4, - 3)
So by Pythagorean theorem
The distance is 10