The function f (x) = x squared minus one is a decreasing function ～

The function f (x) = x squared minus one is a decreasing function ～

Let a be less than B, f (a) = a ^ 2-1, f (b) = B ^ 2-1
f(a)-f(b)=a^2-1-b^2+1=a^2-b^2=(a+b)(a-b)
So, B is less than A-0, B is less than A-0,
By definition, f (x) = x ^ 2-1 is a decreasing function on (negative infinity, 0)
Decreasing function
F (x) = x * X-1 (negative infinity, 0)
Let X1 and X2 belong to (negative infinity, 0) X10
So function f (x) = x squared minus one is a decreasing function ～
It is known that the solution set of the inequality ax-3x + 2 < 0 is a = (x | 1 < x < b) (1) to find the value of A.B (2) to find the function f (x) =（
By using Weida's theorem, we can know that the two equations are 1 and B, then, 1 + B = 3 / A, 1 * b = 2 / A, we get a = 1, B = 2 function f (x) = x-3x + 2
It is known that Mn is opposite to each other, PQ is reciprocal to each other, and a = 2 (M + n / fractional line / 2003A) - 2001pq + (1 fractional line 4) a is the second power
Mn is opposite to each other
m+n=0
PQ is reciprocal to each other
pq=1
The second power of a = 2 (M + n / fractional line / 2003A) - 2001pq + (1 fractional line 4) a
A = the second power of 2 (0 / fractional line / 2003A) - 2001 * 1 + (1 fractional line 4) a
A = - 2001 + (1 fraction 4) the second power of a
The second power of a-4a-8004 = 0
Let f (x) = 3x + 12 / X (x ≠ 0)
This is the check (Nike) function
The bottom of the third quadrant is x = - 2
So, when x = - 2, f (x) has a maximum, f (- 2) = - 12
f(x)'=3-12/x^2;
Let f (x) '= 0, x = 2, - 2;
X
X2-x + 1 / x = 7, find the fourth power of X + the square of X + the square of 1 / X
If x 2-x + 1 is x = 7, then: X 2-x + 1 = 1 / 7, we can get x + x 1 / 7 = 8 / 7, that is: the reciprocal of the fourth power of X + the square of X + 1 / 1 is the fourth power of X + the square of X + 1 / 7, which is reduced to: the square of X + 1 + the square of x = (x + x 1 / 1) = (x + x 1 / 1)'s Square-1
1. It is known that the positive real number x satisfies the inequality log2 (x + 6)
The range of function y = log2 (X & sup2; - 2x-3) is X & sup2; - 2x-3 > 0, so x > 3 or x < - 1 Let f (x) = x & sup2; - 2x-3 = (x-1) & sup2; - 4 because f (x) > 0, so y = the value of log2 (X & sup2; - 2x-3)
X>4
Three rational numbers a, B, C satisfy that ABC is less than 0 and a + B + C is greater than 0. When x = | a | / A + | B | / B + | C | / C, find the value of the 19th power - 92x + 2 of the value x of the algebraic formula
The steps are as follows:
ABC < 0, a + B + C > 0, only one of a, B, C is negative (less than 0), the other two are positive (greater than 0)
The reasons are as follows: if two numbers are negative, one is positive or three are positive, the formula abc0 is not satisfied
When a is negative: x = - A / A + B / B + C / C = 1
x^19 - 92x + 2 = -89
When B is negative: x = A / A + (- b) / B + C / C = 1
x^19 - 92x + 2 = -89
When C is negative: x = A / A + B / B + (- C) / C = 1
x^19 - 92x + 2 = -89
Final x ^ 19 - 92x + 2 = - 89
∵abc＜0，a+b+c＞0
Two positive numbers and one negative number in a.b.c
∴ X=|a|/a+|b|/b+|c|/c
=1 + 1-1 (if any number a, B, C is negative, then the ratio of its absolute value to itself is - 1)
=1
The 19th power of X - 92x + 2 = 1-92 + 2
=-89
Given that the range of F (x) = x ^ 2 + ax + B is [0, positive infinity], if the solution set of the inequality f (x) < C about X is (m, M + 6), then the value of the real number C is zero
△=a^2-4b=0
a^2=4b,x^2+ax+a^2/4
If the rational numbers a, B and C satisfy / A-1 / + / B + 3 / + / 3c-1 / = 0, find the power of (ABC) to the 9th power of (a) × the 3rd power of B?
∵ to make | A-1 | + | B + 3 | + | 3c-1 | = 0, there must be | A-1 | = 0, | B + 3 | = 0, | 3c-1 | = 0
∴ a=1,b=-3,c=1/3
(abc)^2009÷[(a)^9×(b)^3]
=[1×(-3)×（1/3）]^2009÷[1^9×(-3)^3]
=(-1)^2009÷（-27）
=1/27
/a-1/+/b+3/+/3c-1/=0
To meet the needs of the above formula
a-1=0
b+3=0
3c-1=0
The solution is a = 1, B = - 3, C = 1 / 3
So the 2009 power of (ABC) / (the 9th power of a × the 3rd power of B)
=[1*(-3)*(1/3)]^2009÷[1^9×(-3)^3]
=(-1)^2009÷[1×(-27)]
=(-1)÷(-27)
=1/27
∵/a-1/+/b+3/+/3c-1/=0，
∴/a-1/≥0，/b+3/≥0，/3c-1/≥0.
∴/a-1/=0，/b+3/=0，/3c-1/=0.
∴a=1,b=-3,c=1/3.
The 2009 power of (ABC) / (the 9th power of a × the 3rd power of B) = the 2009 power of [1 * (- 3) * 1 / 3] / [1 * (- 27)] = - 1 ÷ (- 27) = 1 / 27
Known function f (x) = log2 (x + 4 / x) solution inequality f (x) is greater than or equal to log22x
log2(x+4/x)≥log22x
Because log2 x is a monotone increasing function
So we have to solve the inequality
That is to solve the system of inequalities
2x>0
x+4/x>0
x+4/x≥2x
The solution is 0