It is known that the domain of definition of function y = f (x) is a closed interval from 0 to 1, if 0

It is known that the domain of definition of function y = f (x) is a closed interval from 0 to 1, if 0

The domain satisfies:
0=

If the domain of function f (x) is a closed interval from - 3 to 1, then what is the domain of function g (x) = f (x) + F (- x)
Let f (x) be a closed interval from - 3 to 1
Then what is the domain of the function g (x) = f (x) + F (- x)

The domain of F (x) is [- 3,1]
g(x)=f(x)+f(-x)
So - 3

It is known that the domain of F (3x + 1) is a closed interval - 1,3. Find the domain of F (x)

Closed interval-2,10

Let the domain of function y = f (x) be interval [a, b], and G (x) = f (x + 1), then the domain of function g (x) is interval ()
What is the relationship between F (x) and G (x)?

The domain of G (x) should be (A-1, B-1). F (x + 1) can be regarded as the figure after the image of F (x) has been translated one unit length to the negative direction of X axis. After translation, the domain of F (x + 1) is (A-1, B-1), so the definition of G (x) is (A-1, B-1)

Let the domain of definition of function y = f (x) be interval [a, b], and G (x) = f (x + 1), then the domain of definition of function g (x) is interval, Xie

The domain of function y = f (x) is interval [a, b], and the domain of F (x + 1) is a ≤ x + 1 ≤ B, so A-1 ≤ x ≤ B-1, G (x) = f (x + 1), so the domain of function g (x) is interval [A-1, B-1]

Find the definition, range and monotone interval of the following functions,
Make it clear
1、 Y = log2 (x's second power + 2x + 5) 2. Y = log one third (- X's second power + 4x + 5) 3. Y = log2 (x's second power - 4x) 4. Y = log one half (x's second power - 6x + 17)

1.x^2+2x+5=(x+1)^2+4>=4
Definition field R, value field is greater than or equal to 2,
Monotone interval x = - 1 monotone increasing
2.-x^2+4+5=-(x-2)^2+9

Find the definition, range and monotone increasing interval of the following functions
(1) Y = 2Sin (quarter-x)
(2) Y = Log1 / 2 bottom SiNx

(1)
Domain of definition: X ∈ R
Range: - 1 ≤ sin (π / 4-x) ≤ 1 - 2 ≤ 2Sin (π / 4-x) ≤ 2
The range is [- 2,2]
y=2sin（π/4-x）=-2sin（x-π/4）
x-π/4∈[π/2+2kπ,3π/2+2kπ] x∈[3π/4+2kπ,7π/4+2kπ] k∈z
Monotone increasing interval [3 π / 4 + 2K π, 7 π / 4 + 2K π] K ∈ Z
(2) Y = Log1 / 2 bottom SiNx
Domain SiNx > 0 x ∈ (2k π, π + 2K π)
Range: 0 < SiNx ≤ 1
0=log1/2(1)≤log1/2(sinx)→+∞
The value range is [0, + ∞)
Monotone increasing interval is decreasing interval when SiNx is greater than zero
x∈[π/2+2kπ,π+2kπ) k∈z

Find the following function definition, range, monotone interval
1: The logarithm of (8-2x) with base 2 of y = log (note x is superscript)
2: Y = the logarithm of (x2 + 2x + 3) whose base is half of log
The second is - x2

1. If the domain is 8-2x > 0, X is obtained

The domain of the function y = x + 2 / x2 + 2x + 3

It is required that X & # 178; + 2x + 3 ≠ 0, i.e. (x + 1) &# 178; + 2 ≠ 0, then constant holds, so the definition field is r, that is (- ∞, + ∞)

Let y = f (x) be defined as R, and f (x1 + x2) = f (x1) + F (x2) for any x 1 and x 2 belonging to R. if x > 0, then f (x) is a function of R

Because for any X1 and X2, f (x1 + x2) = f (x1) + F (x2)
Let X1 = 4, X2 = - 4, then f (0) = f (4) + F (- 4), and f (0) = f (0) + F (0) = 0
Then we know that f (4) = - f (- 4), and if x is any number, then it is an odd function
Then X0
For any number X1 > x2 > 0, f (x1 + x2) = f (x1) + F (x2), X1 + x2 > X1 > X2, but f (x1), f (x2) are less than 0
Then f (x 1 + x 2) is smaller than any of them, then f (x 1 + x 2) is a decreasing function in x > 0, then f (x) is a decreasing function
Then when x is - 4,4, there are maximum and minimum
Then the minimum value is - 2 and the maximum value is 2