Image properties of higher one function?

Image properties of higher one function?

Therefore, G (x) = - QX ^ 4 (2q-1) x ^ 21 is a decreasing function on the interval (- ∞, - 4], and an increasing function on (- 4,0), that is, G (x) = - QT ^ 2 (2q-1) t 1 is an increasing function on [16, ∞)

1 find the maximum (minimum) value of the function f (x) = | X-2 | - | x + 1 | When x is greater than or equal to 0, f (x) = 2x-7, then when x is less than 0, f (x) is even= If the odd function f (x) defined on R satisfies f (x + 2) = - f (x), then f (6) =?

1. Method 1 is to do according to the number axis, the distance to 2 minus the distance to - 1 point, look on the number axis to know the answer. Method 2 is divided into three types of discussion: X

x∈[0,1] Ask for: Y = the range of (x + 1) - 1-x under the radical That is, the range of y = (√ x + 1) - (√ 1-x) The answer I want is y ∈ [0, √ 2] That is, the range of y = [√ (x + 1)] - [√ (1-x)]

The answer is right
In fact, it is very easy to divide the formula into two parts. The first part of the minus sign is the increasing function, and the second half is the subtracting function. Because of the relationship between the minus sign, y is an increasing function. And we know the range of X, so we can find the range of values

What are the properties of power functions?

For y = x, the character "a" is a constant, all passing through the point (1,1)
The image only appeared in quadrant 1.2.3,
On the right side of the line x = 1, the larger the exponent, the higher the image,
Between the Y-axis and x = 1, the larger the exponent, the lower the image

What are the definition and range of arcsine, arccosine, arctangent and arccotangent functions?

Anti sine function: y = arcsinx x ∈ [- 1,1] range is | arcsinx ≤ π / 2
Inverse cosine function: y = arccosx x ∈ [- 1,1] range is 0 ≤ arccosx ≤ π
Arctangent function: y = arctanx x ∈ [- ∞, + ∞] range is | arcstanx | π / 2
Inverse cotangent function: y = arccotx x x ∈ [- ∞, + ∞] range is 0 ＜ arccotx ＜π
I wish you a happy study!

The definition domain of Cotx function y = Cotx is? Cotx = cosx / SiNx; so SiNx ≠ 0; so x ≠ K π Cotx = 1 / TaNx (x ≠ 0.5 π + K π); and TaNx ≠ 0 (x ≠ K π); therefore, X ≠ 0.5K π Which one is right

The first is right
Cotx is defined as Cotx = cosx / SiNx
Cotx = 1 / TaNx is derived from the definition of Cotangent, which is true only if both tangent and cotangent are defined
Therefore, if we infer the definition domain of Cotx = 1 / TaNx, we will omit the parts whose tangent has no definition (tangent infinity), and whose cotange has a definition (cotange is 0)
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The definition domain, range, periodicity, parity and monotonicity of the function y = Cotx are discussed

Fixed: (K π, (K + 1) π)
Range: R
Week: π
odd
Simple subtraction:: (K π, (K + 1) π)

How to find the monotone interval of function What is the monotone interval of F (x) = - 1 / X-1 How did you get it Why do you do this

Derivation~
Judging by the relationship between derivative function and 0

How to find monotone interval of piecewise function

However, in the interval, but decreasing, and y = 1 / ︱ x, this function, in x < 0, is increasing, x0 is decreasing
So monotonicity is possible. We need to discuss it by category
I think for your supplementary question, it should be said in this way
To sum up, 1. The functions studied at present are generally monotonic, but not necessarily global monotone. Some intervals can be increased and some intervals reduced (such as cos function)
2. There is no necessary relationship between the piecewise interval and the monotone interval of piecewise function. In an interval of a piecewise function, there can be an increase or a decrease. In a monotone interval, it can also be segmented

Steps of finding monotone interval of function Please use the method of senior one, don't use derivative

You should be asked about the monotone interval of a complex function: the first step is to determine the domain of definition; the second step is to divide the original function into two functions (more than three functions are the same, but generally can not be touched), calculate their monotone interval respectively, mark the partition node on the number axis, and then judge the increase or decrease in the partition