Find the function y = sin ^ 2x + asinx-1 / 2 (a is a constant, and a

Find the function y = sin ^ 2x + asinx-1 / 2 (a is a constant, and a

If we set SiNx to t, it's actually a substitution,
Y = T ^ 2 + AT-1 / 2 Formula
y=(t+a/2)^2-a^2/4-1/2
Because t = SiNx, the starting value ranges from - 1 to 1
So let's talk about a when - 2
Let a be a constant and a > 0,0=
If SiNx = t, then - 1 ≤ t ≤ 1, the original expression is y = - t * T-2 * a * t,
When the axis of symmetry of a function is t = - a = 1, - A
y=cos^2x-2asinx-1=1-sin^2x-2asinx-1=-sin^2x-2asinx=-(sinx+a)^2+a^2
1. When a > 1, ymax = f (- 1) = - (A-1) ^ 2 + A ^ 2 = 2a-1, yman = f (1) = - (1 + a) ^ 2 + A ^ 2 = - 2a-1
2. When 0
Given that the set a = {kx2-8x + 16 = 0} has only one element, try to find the value of the real number k, and use the enumeration method to represent the set a
When k = 0, the original equation becomes - 8x + 16 = 0, x = 2, then set a = {2}; when k ≠ 0, to make the quadratic equation kx2-8x + 16 = 0 have a real root, we need △ = 64-64k = 0, that is k = 1. At this time, the solution of the equation is X1 = x2 = 4. Set a = {4}, which satisfies the problem. In conclusion, the value of real number k is 0 or 1, when k = 0, set a = {2}; when k = 1, set a = {4}
If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, we can find f (x)
Let's have a try!
Because f (x) is a linear function, Let f (x) = ax + B
Therefore:
f(x+1)=ax+a+b
f(x-1)=ax-a+b
Substituting the given relation, we can get the following conclusion
3ax+3a+3b-2ax+2a-2b=2x+17
The results are as follows
ax+5a-b=2x+17
Comparing the two sides of the equation, the undetermined coefficient is obtained
A=2
B=7
So f (x) = 2x + 7
I don't know if my calculation is wrong, or if the higher people have a better solution? I'll throw a brick to attract jade~
If there is only one element a in the set a composed of the roots of the equation x + X + B = 0, find the value of a + B
The most detailed is the best
-(A-1) / 2 = a, B equals the square of A
How did you get here
The equation has only one solution
Then - (A-1) / 2 = a, B equals the square of A
The solution is a = 1 / 3, B = 1 / 9
Then a + B = 4 / 9
When the equation is in the form of x2-2mx + M2 = 0, there is only one m root
Use this form to bring in the equation in the problem
The analytic expression of F (x) is obtained when f (x) is a function of degree and 3f (x + 1) - 2F (x-1) = 2x + 17 is satisfied
Because f (x) is a linear function
So let f (x) = ax + B
From the meaning of the title: 3 [a (x + 1) + b] - 2 [a (x-1) + b] = 2x + 17
Combining, we get: 3ax + 3A + 3b-2ax + 2a-2b = 2x + 17
ax+5a+b=2x+17
Because this is an identity, we have:
ax=2x
5a+b=17
The solution is a = 2
B=7
So f (x) = 2x + 7
The square of the equation x = the set of all the real roots of X
-1 is not the root of the equation
It is known that f (x) is a linear function, and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17. The process of finding f (x)? Is detailed and clear!
Let f (x) = KX + B  f (x + 1) = K (x + 1) + B = KX + K + B (where x is replaced by X + 1 in the analytical formula) 〉 f (x-1) = K (x-1) + B = kx-k + B (where x is replaced by X-1 in the analytical formula) ∧ 3f (x + 1) - 2F (x-1) = 2x + 17 ∧ 3kx + 3K + 3b-2kx + 2k-2b = 2x + 17 ∧ KX + (5K + b) = 2x
It is known that the element of the set a is the root of the equation AX's Square - 3x + 2 = 0. If there is only one element in a, the value range of a is obtained
There is only one element in a
Then the equation AX & sup2; - 3x + 2 = 0 has only one solution
(1) If a = 0, the equation is - 3x + 2 = 0
(2) If a ≠ 0, then the equation is a quadratic function
Discriminant △ = 9-8a = 0, a = 9 / 8
A = 0 or a = 9 / 8
If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, then f (x)=____
Let f (x) = KX + B, then f (x + 1) = KX + K + B, f (x-1) = kx-k + B, substituting into the given equation, we get: 3kx + 3K + 3B - (2kx-2k + 2b) = 2x + 17, that is: KX + 5K + B = 2x + 17 corresponds to the same kind of coefficient (i.e. undetermined coefficient method) k = 2,5k + B = 17, we get: k = 2, B = 7; so: F (x) = 2x + 7, if you don't understand, please hi me