Given that f (x) = ax / x ^ 2-1, a ≠ 0, if both the domain of definition and the domain of value of the function are [- 1 / 2,1 / 2], the value of a is obtained

Given that f (x) = ax / x ^ 2-1, a ≠ 0, if both the domain of definition and the domain of value of the function are [- 1 / 2,1 / 2], the value of a is obtained

F (x) = ax / x ^ 2-1, a ≠ 0, if the definition field of function is [- 1 / 2,1 / 2],
-2/3*a

The application of function in daily life. One example of first-order function, second-order function, exponential function, power function and logarithmic function
Life examples

First order function: physical application
Quadratic function: physical application
Exponential function: the number of bacteria changes with time
Power function: compound interest on bank deposits
Logarithmic function: in reality, the number of certain organisms changes with time
Note: in accordance with the power function and logarithmic function must be y = a ^ x, y = loga (x) (a > 0, a ≠ 0)

Let a be a constant, a > 1,0 ≤ x ≤ 2 π, then what is the maximum value of the function f (x) = cos ^ 2 + 2asinx-1?
I can also turn it into a vertex form. Why can I get the maximum when SiNx = 1 instead of when SiNx = - 1

f'(x)=-2cosx*sinx+2acosx
Let f '(x) = 0
That is SiNx = a
Then when SiNx = a, f (x) is the extremum
And a > 1, - 1 ≤ SiNx ≤ 1
So the maximum value of SiNx is 1
f(x)=1-a^2+2*a*a-1
=a^2
=1
As you said, if SiNx = - 1, that is, a = - 1, does not satisfy the condition of a > 1

Let a be a constant and a ＞ 1,0 ≤ a ≤ 2 π, then the maximum value of the function f (x) = cos & # 178; X + 2asinx-1 is

Square of a
Let SiNx be t, and a solution of quadratic equation of one variable will do

Let a be a constant and a ＞ 10 ≤ x ＜ 2 π, then the maximum value of F (x) = cos ^ 2x + 2asinx-1 is

f(x)=-(sinx)^2+2asinx=-(sinx-a)^2+a^2
When x = π / 2, SiNx = 1, the maximum value of F (x) is f (π / 2) = a ^ 2 - (1-A) ^ 2

Given that x belongs to [0,2pai], a is a constant, find the maximum value of the function y = cos ^ 2x + 2asinx-1

y=cos^2x+2asinx-1
=-sin²x+2asinx
=-(sinx-a)²+a²
1.a>1
Maximum = - 1 + 2A (when SiNx = 1)
two
-1

Let a be a constant, and a > 1, 0 be less than or equal to x, 2 be less than or equal to, and find the maximum value of the function f (x) = cos square x + 2asinx-1
Symbols don't work. Let's see

f（x)=cos^2x+2asinx-1=-sin^2x+2asinx
Let t = SiNx, f (x) = - T ^ 2 + 2at | t | ≤ 1
For this quadratic function, when t = a, find the maximum value. But a > 1, so take the maximum value when t = 1, substitute t = 1 into the function, and get the maximum value as - 1 + 2A

Function f (x) = the square of X, what is cosx
Given sin (PAI + a) = 5 / 3, a is the fourth quadrant angle, then cosa is equal to how much, and this! 3Q
Function f (x) = sinxcosx minimum positive period is more than this!

What is the square of function f (x) = x, the square of function f (- x) = (- x), the square of COS (- x) = x, the square of cosx even function we know sin (PAI + a) = - Sina = 5 / 3, Sina = - 3 / 5 A is the fourth quadrant angle, cosa > 0, sin ^ 2A + cos ^ 2A = 1, cosa = 4 / 5, function f (x) = sinxcosx = 1 / 2 * sin2a minimum positive period

What is the function y = x square + cosx?

Even function
y（-x）=（-x）^2+cos（-x）=x^2+cosx=y（x）
And the domain of definition is r symmetric about the origin
So it's an even function

Period of the function FX = cosx Square-1 / 2?