What is the range of the function f (x) = x & # 178; - 2x, X ∈ (- 1,4)?

What is the range of the function f (x) = x & # 178; - 2x, X ∈ (- 1,4)?

f(x)=(x-1)²-1
The opening is upward and the axis of symmetry is x = 1
In the interval (- 1,4], when x = 1, take the minimum value - 1;
When x = 4, the maximum value is 8
So the range is [- 1,8]

The range of function y = x & # 178; + 2X-4, - 2 ≤ x ≤ 2 is?

y=x²+2x-4=(x+1)²-5>=-5
When x = - 1, the minimum value of Y is - 5
Because | 2 - (- 1) | > | - 2 - (- 1) |, that is, x = 2 is far away from x = - 1
So when x = 2, y has a maximum of 3 & # 178; - 5 = 4
So the range is [- 5,4]

Find the range of the following functions: (1) y = 2x-3 + √ 13-4x (2) y = 2 - √ - x ^ 2 + 4x (x ∈ [0,4])

1) Let √ (13-4x) = t > = 0,
Then x = (13-t ^ 2) / 4
y=(13-t^2)/2-3+t=1/2*[-t^2+2t+7]=1/2*[ -(t-1)^2+8 ]
When t = 1, ymax = 4
So the range is y

F (x) = (the square of X - 2x + 2) divided by X in the range of (0,0.25]
A few more similar topics

f(x)=(x²-2x+2)/x
=x+2/x-2
This is the hook function
For y = x + K / x, k > 0
The increasing intervals are (- ∞, - √ K) and (√ K, + ∞)
The subtraction intervals are (- √ K, 0) and (0, √ K)
What to remember in senior one
∴x∈(0,1/4]
F (x) = x + 2 / X-2 is a decreasing function in (0, √ 2)
The minimum value of F (x) is f (1 / 4) = 1 / 4 + 8-2 = 25 / 4
The value range is [25 / 4, + ∞)
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Find the range 1, y = x square + 1 / x square - 1,2, y = 2x square + 4x-7 / x square + 2x + 1

y=(x²+1)/(x²-1)
=1+2/(x²-1)
x²-1>=-1
Function range (1, + ∞) ∪ (- ∞, - 1]
y=(2x²+4x-7)/(x²+2x+1)
=[2(x+1)²-9]/(x+1)²
=2-9/(x+1)²
Function range (- ∞, 2)

How to find the monotone decreasing interval of X + 2x-3 under y = radical

By using the monotonicity of composite function,
t=x²+2x-3,y=√t,
(1) First find the domain of definition, t ≥ 0
∴ x²+2x-3≥0
Ψ x ≥ 1 or X ≤ - 3
（2） t=x²+2x-3
The opening of the image is upward,
It is an increasing function on [1, + ∞) and a decreasing function on (- ∞, - 3]
And y = √ t is an increasing function in [0, + ∞)
Making use of the principle of the same increase but different decrease
The monotone decreasing interval of X + 2x-3 under y = root is (- ∞, - 3]

The monotone interval of y = (radical 2-1) ^ - x ^ 2 + 2x + 3 is?
The monotone increasing interval of y = (radical 2-1) ^ - x ^ 2 + 2x + 3 is?

The monotone increasing interval of y = (√ 2-1) ^ (- x ^ 2 + 2x + 3) is?
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How to find the monotone interval of y = 1-radical (x-3x + 2)

How to find the monotone interval of y = 1-radical (x-3x + 2)
Let's start with the domain
X ^ 2-3x + 2 "0 = > (X-2) (x-1)" 0 = > x "2. Or X" 1 "
And x ^ 2-3x + 2 = (x ^ 2-3x + 9 / 4) + 2-9 / 4 = (x-3 / 2) ^ 2-1 / 4
G (x) = x ^ 2-3x + 2 is monotonically decreasing on (negative infinity, 1) and increasing on (positive infinity, 2)
therefore
Y = 1-radical (x-3x + 2)
Monotonically increasing on (negative infinity, 1), monotonically decreasing on (positive infinity, 2)

Monotone interval of function y = radical (x's square + x)

x²＋x≥0
x（x＋1）≥0
X ≥ 0 or X ≤ - 1
x²＋x=（x＋1/2）²-1/4
therefore
X ≤ - 1 decreasing, i.e. decreasing interval (- ∞, - 1]
When x ≥ 0, the interval [0, + ∞) increases

Find the stationary point and extreme point of the function z = x ^ 3 + y ^ 3-3 (x ^ 2 + y ^ 2)