Y = sin | x | is an even function with a period of 2 π

Y = sin | x | is an even function with a period of 2 π

Y = sin | x | is even function but not periodic function

If y = sin ((1 / 2) x + W) is an even function, what is the requirement of W

If even function sin (1 / 2 * x + W) = sin (- 1 / 2 * x + W) holds constant, then 1 / 2x + W = - 1 / 2 * x + W + 2K π or 1 / 2x + W = - (- 1 / 2 * x + W) + 2K π + π 1 / 2x + W = - 1 / 2 * x + W + 2K π x = 2K π, not 1 / 2x + W = - (- 1 / 2 * x + W) + 2K π + π 1 / 2x + W = 1 / 2 * X-W + 2K π + π w = k π + π / 2, so w = k π + π / 2

If y = sin (2 α + φ) is even, then φ is equal to

Y = sin (2 α + φ) is even function
Then the y-axis is the symmetry axis of the function
Because the trigonometric function takes the maximum value at the axis of symmetry
So sin (0 + φ) = ± 1
So φ = 2K π ± π / 2

If f (x) = x ^ 2 + 4x + 3, f (AX + b) = x ^ 2 + 10x + 24, 5a-6 =?

Substituting ax + B into f (x), we get
(ax+b)^2+4(ax+b)+3
=(ax)^2+2abx+b^2+4ax+4b+3
=a^2x^2+(2ab+4a)x+b^2+4b+3
Compared with type 2, it's better
a^2=1
2ab+4a=10
b^2+4b+3=24
Joint solution
A = 1, B = 3 or a = - 1, B = - 7
So 5a-b = 5 * 1-3 = 2 or 5a-b = 5 * (- 1) - (- 7) = 2
In conclusion, 5a-b = 2
The solution to this problem is as follows
Original function f (x) = x ^ + 4x + 3 = (x + 3) (x + 1)
And the function f (AX + b) = x ^ + 10x + 24 = (x + 6) (x + 4) = (x + 3 + 3) (x + 3 + 1)
So ax + B = x + 3
A = 1, B = 3
So 5a-b = 2
There is no fixed method for such questions. It mainly depends on whether you can master the meaning and properties of functions. You can improve this aspect by doing questions!

Given that a and B are constants, if f (x) = x2 + 4x + 3, f (AX + b) = x2 + 10x + 24, then the value of 5a-b is obtained

From F (x) = x2 + 4x + 3, f (AX + b) = x2 + 10x + 24, we get (AX + b) 2 + 4 (AX + b) + 3 = x2 + 10x + 24, that is, a2x2 + 2abx + B2 + 4ax + 4B + 3 = X2 + 10x + 24

4x-3 (5-x) = 6, how fast is the equation solving?

4x-3(5-x)=6
4x-15+3x=6
7x-15=6
7x=21
x=3

The solution of equation 0.4x + 3 + 0.5 = 7.5 and equation x + m / 0.2 = 40 are equal. Find the value of M

0.4x+3+0.5=7.5
x=10
x+m/0.2=40
10+m/0.2=40
m/0.2=30
m=6

It is known that the equation (5 + 3M) x - (2 + m) = 7 has the same solution as the equation 4x-16 = 0, and the value of M is obtained

4x-16=0
4x=16
x=4
(5+3m)x-(2+m)=7
20+12m-2-m=7
11m=9-20
11m=-11
m=-1

The solution of equation 0.4x + 3x0.5 is the same as that of equation x + m divided by 0.1 = 20

0.4x+3×0.5=0
x=-1.5/0.4=-3.75
When substituting x = - 3.75 into x + m △ 0.1 = 20, then
-3.75+m÷0.1=20
m÷0.1=20+3.75
m=2.375

The equation o.4x + 1.5 = 7.5 has the same solution as the equation x + m divided by o.1 = 20

According to the first equation, x equals 15. Substituting x equals 15 into the second equation, m equals - 10