What's the number of even functions X and X? Please be more detailed

What's the number of even functions X and X? Please be more detailed

Even function
f(-x)=f(x)
-(a-1)x³+3x²-bx+c=(a-1)x³+3x²+bx+c
So (A-1) x & # 179; + BX = 0
This holds no matter what value x takes
So A-1 = 0, B = 0
That is, a = 1, B = 0
F (x) = (A-1) x & # 179; + 3x & # 178; + BX + C are even functions,
f(-x)=-(a-1)x³+3x²-bx+c=f(x)=(a-1)x³+3x²+bx+c
a-1=-(a-1)
a-1=0
A=1
b=-b
B=0
a=1 b=0
f(1)=f(-1)
f(2)=f(-2)
Get; two equations, solve out on the line.
In fact, as long as we observe the power exponent of X, the even number remains, and the coefficient of odd number becomes 0. This is a simple method.
∵ function f (x) is an even function ∵ f (- x) = f (x)
∴﹣(a－1)x³＋3x²－bx＋c＝(a－1)x³＋3x＋bx＋c
∴﹣(a－1)＝a－1 ﹣b＝b
∴a＝1 b＝0
If the function f (x) = - X & # 178; + BX + C is even and f (0) = 2, find the analytic expression of F (x)
f(-x)=f(x)
-x^2-bx+c=-x^2+bx+C
B=0
And f (0) = 2, C = 2
f(x)=-x^2+2
It is known that the quadratic function f (x) = ax & # 178; + BX (a ≠ 0) satisfies the condition f (1-x) = f (1 + x) and the equation f (x) = x has equal roots
Is there a real number m, n (m < n) such that the domain of F (x) is [M, n] and the domain of F (x) is [3M, 3N]
From F (1-x) = f (1 + x), we know that the axis of symmetry is x = - B / 2A = 1. From F (x) = x, we get ax & # 178; + (B-1) x = 0 has equal roots, so (B-1) ^ 2 = 0, that is, B = 1, so a = - 1 / 2, so f (x) = - 1 / 2x & # 178; + X
1. If M
If the solution of equation 3 (x + 4) = 2A + 5 about X is larger than that of equation [(4a + 1) x] / 4 = [a (3x-4)] / 3 about X, the value range of a is obtained
3(x+4）=2a+5
3x+12=2a+5
3x=2a-7
x=(2a-7)/3
[（4a+1）x]/4=[a(3x-4)]/3
3(4a+1)x=4a(3x-4)
12ax+3x=12ax-16a
3x=-16a
x=-16a/3
(2a-7)/3＞-16a/3
2a-7＞-16a
18a＞7
a＞7/18
It is known that the solution of the equation KX = 4-x about X is a positive integer
The original equation is transformed into KX + x = 4, that is, (K + 1) x = 4, the solution of the equation KX = 4-x about X is a positive integer, and the product of K + 1 and X is 4, then K + 1 = 4 or K + 1 = 2 or K + 1 = 1 can be obtained, and the solution is k = 3 or K = 1 or K = 0. Therefore, the integer solution of K can be obtained as 0, 1, 3
Given the complete set u = R, set a = {x | x ^ 2-2x > 0}, B = {x | y = LG (x-1)}, (CUA) ∩ B =?
Set a = {x | x ^ 2-2x > 0} = {x | x2}
CuA={x|0≤x≤2}
B = {x | y = LG (x-1)} is the domain of the function y = LG (x-1)
The solution of X-1 > 0 is x > 1
So B = {x | x > 1}
∴(CuA)∩B={x|1
analysis
Set a x (X-2) > 0
x> 2 or X0
X>1
therefore
CUA intersection B = 1
Given that x = 1, y = 2 is the solution of the system of equations ax-y = 1, 3Y = by = - a about X, y, find the value of (a + b) to the power of 2013
emergency
The solution is x = 1, y = 2, which is a system of equations ax-y = 1,3x + by = - A
Then a * 1-2 = 1,3 * 1 + 2B = - A
That is, a = 3, B = - 3
That is, a + B = 0
That is the power of (a + b)
=The power of (0)
=0
The answer is to the power of 6
Sixth grade circle area, perimeter formula, who can write it
Perimeter: 2x radius x3.14 = diameter x3.14
Area: PI (3.14) x radius x radius
Area: π R & # 178; (R is radius)
Perimeter: 2 π R (R is radius)
Given that x = - 1, y = 2 is the solution of the binary linear equations 3x + 2Y = a, 5x + 2Y = B, how much is the 2014 power of (a + 2b)
Substituting x = - 1, y = 2,
The solution is a = 1, B = - 1
a+2b=-1
(-1)^2014=1
That is, the 2014 power of (a + 2b) is 1
X=-1,y=2
∴a=1 b=-1
2014 power of (a + 2b) = 2014 power of - 1 = 1
complete!
The steps of solving linear equation of one variable are as follows: ① remove brackets; ③ transfer terms; ④ merge similar terms; ⑤ change coefficient to 1
The steps of solving linear equation of one variable are as follows: ① remove the denominator; ② remove the bracket; ③ transfer the term; ④ merge the similar terms; ⑤ change the coefficient to 1