Why f (π / 3-x) = f (π / 3 + x), it shows that a symmetry axis of function image is x = π / 3, Given the function f (x) = (radical 5) sin (2x + φ), for any x, f (π / 3-x) = f (π / 3 + x)

Why f (π / 3-x) = f (π / 3 + x), it shows that a symmetry axis of function image is x = π / 3, Given the function f (x) = (radical 5) sin (2x + φ), for any x, f (π / 3-x) = f (π / 3 + x)

Knowledge: if f (x) satisfies f (a + x) = f (b-X), then a symmetry axis of F (x) is x = (a + b) / 2
Corollary: if f (x) satisfies f (a + x) = f (A-X), then a symmetry axis of F (x) is x = a
The proof is a little complicated, just remember the conclusion

In the symmetry axis of the function f (x) = sin (2x - π / 3), the equation of the nearest symmetry axis to the Y axis is?
x=kπ/2+5π/12
And then what is k?
The answer is - π / 12, 5 π / 12 is wrong

K is - 1, so x = 5 π / 12 - π / 2 = - π / 12

Given the symmetry axis X = 1 of the function y = f (x), and the function has three zeros, what is the sum of these zeros

The axis of symmetry x = 1 of the function y = f (x)
And the function has three zeros
It shows that there is a zero at x0 = 1
The other two zeros are symmetric with respect to x = 1
Let x1

For any two positive real numbers x, y, f (XY) = f (x) + F (y) holds. If f (2) = 1, then f (8)=

f（4）=f（2）+f（2）=2
f（8）=f（4）+f（2）=3

Let y equal to f (x) be a function defined on a positive real number set, and f (XY) equal to f (x) plus f (y), and f (2) equal to 1, then what is the f radical 2?

Let f (2) = f (√ 2) + F (√ 2), then f (√ 2) = half

A symmetry axis equation of the graph of the function y = cos (2x + π 2) is ()
A. x=-π2B. x=-π4C. x=π8D. x=π

The equation of symmetry axis of this function is 2x + π 2 & nbsp; = k π (K ∈ z). When k = 0, x = & nbsp; − π 4

Given the function cos (2a pi / 3) + sin (a-pi / 4) sin (a + pi / 4), we can find the minimum positive period of the function and the equation of image symmetry axis
Finding the minimum positive period of function and the equation of image symmetry axis
Find the range of the function in the interval [- pi / 12, PI / 2]

Y=cos(2a-π/3）+sin(a-π/4)sin(a+π/4)= cos(2a-π/3）+ sin(a-π/4)sin[(a-π/4)+π/2]= cos(2a-π/3）+ sin(a-π/4)cos(a-π/4)= cos(2a-π/3）+1/2*sin(2a-π/2)= cos(2a-π/3）-1/2*cos(2a)= cos(2a) cosπ/3+...

If the function y = 3sin (2x + π 6) is known, then the equation of its axis of symmetry is ()
A. x=0B. x=-π12C. x=π6D. x=π3

From 2x + π 6 = k π + π 2, we can get x = k π 2 + π 6 (K ∈ z), let k = 0, we can get x = π 6, its equation of symmetry axis is x = π 6, so we choose C

Given that the image of quadratic function passes through a point (- 2,0), the ordinate of the intersection point with y axis is - 3, and the symmetry axis is a straight line x = 2, find its function expression

If the image of a quadratic function passes through a point (- 2,0) and the axis of symmetry is a straight line x = 2, we can get that the coordinate of the image of a quadratic function passing through another point on the X axis is (6,0), the ordinate of the intersection point with the Y axis is - 3, and the coordinate of the intersection point with the Y axis is (0, - 3)

Given that the image intersection axis of quadratic function is at (- 1,0) (5,0), what is the equation of symmetry axis of image, and if the opening is downward, what is the maximum value

According to the two formulas, the analytic formula of quadratic function is
Y = a · [x - (- 1)] · (X-5), i.e. y = a · (X & sup2; - 4x-5)
It is shown that y = a · [(X-2) & sup2; - 9]
The equation of axis of symmetry is x = 2;
If the opening is downward, then a is less than 0, so the maximum is - 9a, where a is the quadratic coefficient