High school function problem solving function domain Let the domain of function y = f (x) be [- 2,3], then what is the domain of function f (x) = f (x) + F (- x)?

-2≤x≤3;
-2≤-x≤3;
∴x∈{x|-2≤x≤2}

Given y = f (x) + G (x), where f (x) is a positive proportion function, G (x) is an inverse proportion function, and y = 16 when x = 1 / 3, y = 8 when X-1, the analytic expression of Y is obtained

F (x) is a positive proportional function and G (x) is an inverse proportional function
Let f (x) = k * x; G (x) = A / X;
Then 16 = k * (1 / 3) + A / (1 / 3);
8 = k * 1 + A / 1; (Note: if the original question is x = 1, y = 8, if not, it can be directly substituted into the correct number)
We can get k = 3, a = 5;
y=3x+5/x

Given the quadratic function, & (x) = f (x) + G (x), where f (x) is the positive proportional function of X, G (x) is the inverse proportional function of X, and & (1 / 3) = 16
&(1) = 8, find the expression of & X

Let f (x) = KX, G (x) = B / X
Then & (x) = f (x) + G (x) = KX + B / X
And (1 / 3) = 16
&（1）=8
Substituting the point, we can get k = 3, B = 5
∴ &（x)=3x+5/x

(1) If the function f (x) = 2x ^ 2-mx + 3 is an increasing function when x ∈ [2, + infinity], and a decreasing function when x ∈ (- infinity, 2), then f (1)=
(2) Given that the function y = x is monotonically increasing on [a, + infinity), the value range of real number a is obtained

It is known from the title that x = 2 is the axis of symmetry of F (x)
So B of - 2A = 2
That is (- M) = 2
The solution is m = 8
That is, f (x) = 2x & # 178; - 8x + 3
f(1)=2-8+3=-3
Draw an image and you will know: y = | x | decreases on (- ∞, 0]
Incrementing on [0, + ∞)
So there is a ≥ 0

F (x) = 2x ^ 2-mx + 3 is an increasing function on [- 2, + ∞) and a decreasing function on (- ∞, 2) to find the range of M

First of all, as you said above, your statement is contradictory. I guess the problem should be that (- ∞, - 2) is a decreasing function
Since this is a quadratic function with an opening upward, the axis of symmetry must be the dividing line of increase and decrease. That is to say, there is - 2 = - (- M) / 2 * 2, so m = - 8
Looking forward to further clarification

If f (x) = 2x ^ 2 -- MX + 3 is a decreasing function on (- ∞, - 3), then the range of M is (please write the procedure)

Because the axis of symmetry of F (x) = 2x ^ 2 -- MX + 3 is x = m / 4, and the parabola opening is upward
So if x = - 3
m>=-12

If the function f (x) = 2x ^ 2-mx + 3 is an increasing function at (- 2, + ∞) and a decreasing function at (- 2, + ∞), then the value range of M is

Because it is a quadratic function, we know that its axis of symmetry is x = - 2, that is, x = - B / 2A = - 2. Substituting a and B, we get m = - 8. It is a definite value, not a range

Given the function f (x) = CX / 2x + 3 (x is not equal to - 3 / 2) and f [f (x)] = x, find the value of C
When x = 0, C can go to any value?
Is there something wrong with this question

Because when x = 0, f (0) = C × 0 / (2 × 0 + 3) = 0f [f (0)] = f (0) = 0, the normal solution is: F (f (x)) = C [CX / (2x + 3)] / {2 [CX / (2x + 3)] + 3} multiplication 2x + 3 = C ^ 2x / [2cx + 3 (2x + 3)] = C ^ 2x / [(2C + 6) x + 9] = x, so C ^ 2 = (2C + 6) x + 9 (2C + 6) x = C ^ 2-9

Let f (x) satisfy f (x + 1) - f (x) = 2x + 3 and f (0) = 0, then f (- 2) is equal to

Let x = - 1, then f (- 1 + 1) - f (- 1) = f (0) - f (- 1) = - 2 + 3 = 1, that is, f (- 1) = - 1
Let x = - 2, then f (- 2 + 1) - f (- 2) = f (- 1) - f (- 2) = - 4 + 3 = - 1, that is, f (- 2) = 0

The function f (x) = 2x MX + 3 is an increasing function when x ∈ [- 2, + ∞), and a decreasing function when x ∈ (- ∞, - 2], then f (1) is equal to————

Because x is an increasing function on [- 2, + ∞] and a decreasing function on (- 2, - ∞), when x = - 2, the function f (x) gets the minimum value, that is, x = - 2 is the vertex of the function, and from the vertex coordinates we get - 2 = - B / 2a, that is, M / 4 = - 2, so m = - 8, so f (1) = 2 + 8 + 3 = 13

High school function problem solving function domain Let the domain of function y = f (x) be [- 2,3], then what is the domain of function f (x) = f (x) + F (- x)?