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Try to discuss the number of zeros of function H (x) = f (x + 1) - G (x) in the interval (- 2,0) Given function f (x) = LG (x + 1) 1. If G (x) is an even function and G (x) = g (x + 2), when 0 ≤ x ≤ 1, G (x) = f (x), find the analytic expression of y = g (x) (x belongs to [- 2,0]; 2. Under the condition of (1), the number of zeros of the function H (x) = f (x + 1) - G (x) in the interval (- 2,0) is discussed
1. First find - 1
The image of the function f (x) defined on R is symmetric with respect to points a (a, b) and B (C, d), where C is not equal to the period of a finding f (x)
So f (x-a) = - f (x + a)
Why?
First of all, x-a and X + a are the values of independent variables which are symmetric with respect to X. then, when the independent variables take these two values, the function values are opposite to each other, which means that the function f (x) is symmetric with respect to point (a, 0)
In the first problem, we know that (3x-2y) & sup2; - 10 (3x-2y) + 25 = 0, and find the value of 9x square - 12xy + 4Y & sup2; + 1,
In the second problem, we know that X & sup2; + 2XY + 2Y & sup2; - 6y + 9 = 0 and find the values of X and y
In the third question, we know that a, B and C are three sides of △ ABC, and the cubic power of a squared B-A & sup2; C + B squared C-B = 0, we prove that △ ABC is an isosceles triangle
The fourth problem is known that a, B, C are the three sides of △ ABC, try to determine the sign of the value of the algebraic formula (A & sup2; + B & sup2; - C & sup2;) - 4A & sup2; B & sup2;)
The fifth problem is known that X & sup2; + X-1 = 0, find the value of 5x fourth power + 5x third power + 5x + 8
(1) (3x-2y) & sup2; - 10 (3x-2y) + 25 = 0, so: (3x-2y-5) ^ 2 = 0, the solution is: 3x-2y = 59x ^ 2-12xy + 4Y ^ 2 + 1 = (3x-2y) ^ 2 + 1 = 25 + 1 = 26 (2) x & sup2; + 2XY + 2Y & sup2; - 6y + 9 = 0, so: (x + y) ^ 2 + (Y-3) ^ 2 = 0 (3) a ^ 2b-a ^ 2C + B ^ 2C-B ^ 3 = 0, so: A ^ 2 (B-C) - B ^ 2 (B -
The image of quadratic function takes the straight line x = - 2 as the symmetry axis, and the function has the minimum value - 4
The image of quadratic function takes the straight line x = - 2 as the symmetry axis, and the function has the minimum value - 4, so let f (x) = a (x + 2) ^ 2-4
It also passes through the point (0,1), that is, 1 = a * (0 + 2) ^ 2-4, a = 5 / 4
f(x)=5/4*(x+2)^2-4
If a is a real number, compare the value of (A-1) &# 178; with that of a & # 178; - 4A + 2
If a + b > 0, compare the size of a & # 179; + B & # 179; and a & # 178; B + AB & # 178
(a-1)²-(a²-4a+2)=6a-1
When a is greater than 1 / 6, (A-1) &# 178; greater than a & # 178; - 4A + 2
When a is less than or equal to 1 / 6, (A-1) &# 178; less than or equal to a & # 178; - 4A + 2
A & # 179; + B & # 179; and a & # 178; B + AB & # 178;
a³+b³-（a²b+ab²)
=a³-a²b+b³-ab²
=a²(a-b)+b²(b-a)
=(a-b)(a²-b²)＞0
a³+b³＞a²b+ab²
If the equation (3-m) x ^ 2 | m | - 5 + 2 = 5 is a linear equation with one variable, is the value of m certain?
That is, the degree of X is 1
2|m|-5=1
|m|=3
m=±3
And the coefficient of X is 3-m ≠ 0
m≠3
So m = - 3
X^2-8x+16=0
I want to know (x-4) ^ 2 = 0
How did this step come about
X^2-8x+16=0
(x-4)^2=0
x-4=0
x=4
If the positions of the points representing the two real numbers a and B on the number axis are as shown in the figure, the result of simplification: | A-B | + A + B is______ ．
How to calculate X-1 of X + 1 minus x + 1 of 3x-3 = 2
(x+1)/(x-1)-3(x-1)/(x+1)=2
Multiply both sides by (x + 1) (x-1)
(x+1)^2-3(x-1)^2=2(x^2-1)
4x^2-8x=0
X = 2 or x = 0
Matrix similar positive definite
How to judge the dissimilarity of two square arrays
If a and B can be diagonalized (symmetric matrix)
If and only if the eigenvalues of a and B are the same
If a and B cannot be diagonalized, the necessary and sufficient condition is beyond the scope of linear algebra
Knowledge of λ - matrix (Jordan canonical form) is needed
A. B similar characteristic polynomial equivalence
A. The necessary conditions of B similarity: the same rank, the same eigenvalue and the same trace
RELATED INFORMATIONS
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