The monotone decreasing interval of (- x 2 + 2x + 3) under the function y = radical is

Y = radical (- x ^ 2 + 2x + 3)
Define domain
-x^2+2x+3>=0
x^2-2x-3

Under the radical sign of function y = 2, the monotone increasing interval of - x 2 + 2x + 3 is ---?

First of all, we calculate the monotone interval of - x? + 2x + 3 = - x? + 2x-1 + 4 = - (x-1) ^ 2 + 4 = - (x-1) ^ 2 + 4, and the monotone increasing interval of - (x-1) ^ 2 + 4 can be - (x-1) ^ 2 + 4 ≥ 0, - 1 ≤ x ≤ 3, and the function f (x) = - (x-1) ^ 2 + 4 is monotonically recursive in [- 1,1]

Find the monotone interval of - x 2 + 2x + 3 under y = - radical

y=-√(-x^2+2x+3)
Let u = - x ^ 2 + 2x + 3
Then y = - √ U
Y decreases with the increase of u and increases with the decrease of U
u=-(x-1)^2+4
When x = 1, u decreases with the increase of X
Therefore, when x = 1, y increases with the increase of X, and the monotonic increasing interval is: [1, + ∞)

The monotone decreasing interval of the function f (x) = root of 2x-x 2 is?

Definition domain: 2x-x 2 ≥ 0;
x²-2x≤0；
∴0≤x≤2；
f(x)=√2x-x²=√-(x-1)²+1;
The axis of symmetry is x = 1;
The monotone decreasing interval is [1,2]
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The function f (x) = the fourth power of x minus the square of 3x minus 6x plus 13 minus the fourth power of x minus the square of x plus 1

In this paper, we consider using the geometric method: first, f (x) deformation, f (x) = under the root sign (x-3) ^ 2 + (x ^ 2-2) ^ 2 minus (x-0) ^ 2 + (x ^ 2-1) ^ 2. Note the geometric meaning of this formula: it represents the difference between the distance between the point (x, x ^ 2) and the other two points (3,2) (0,1)

It is proved that the function f (x) = radical 1 + x square - x is a monotone decreasing function on R

1. Derivative method
f'(x)=x/√(1+x^2) -1=[x-√(1+x^2)]/√(1+x^2).
Molecules are always

Given that f (x) = 3x2-5x + 2, find f (- 2) , f (- a), f (a + 3), f (a) + F (3)

f(−
2)＝3×(−
2)2−5×(−
2)+2＝8+5
2，
f（-a）=3a2-5a+2，
f（a+3）=3（a+3）2-5（a+3）+2=3a2+5a+2，
f（a）+f（3）=3a2-5a+2+3×32-5×3+2=3a2-5a+16．

Find the definition domain of the following functions: ① y = the square of x-2x-3; ② y = 1 / 5 of x-3; ③ y = root 3x 2 + 2x-1

① X is all real numbers
②x－5≠0 x≠5
③3x²＋2x－1≥0 (x＋1)(3x－1)≥0 ∴x≥1/3 x≤﹣1

Find the definition domain of function, 1, the square of y = 3x + 6x-12, the absolute value of 2x + 13, y = x + 2 - 1 / 1

The square of y = 3x + 6x-12
x∈R
Y = 2x + 1 3 under radical
2X+13≥0
x∈【-6.5,+∞）
y=1/(|x＋2|-1)
(|x＋2|-1)≠0
x+2≠±1
x≠-3,x≠-1
x∈(-∞,-3）,（-3,-1）,（-1,+∞）

The monotone increasing interval of the function f (x) = x ^ 2-3x + 2 is

Under the radical sign, then x? - 3x + 2 > = 0
(x-1)(x-2)>=0
X=2
The axis of symmetry of X? - 3x + 2 is x = 3 / 2
Opening up
So x > 3 / 2 increases
Combined definition domain
So the increasing interval is (2, + ∞)

The monotone decreasing interval of (- x 2 + 2x + 3) under the function y = radical is