Y = 2X-4 ÷ x + 3 to find the range of function is the value range of Y

Y = 2X-4 ÷ x + 3 to find the range of function is the value range of Y

y=(2x-4)/(x+3)
The inverse method is used
2x-4=yx+3y
(2-y)x =(3y+4)
x=(3y+4)/(2-y)
Because the inverse function of X has a solution, so,
2-y≠0
y≠2
So the range of the original function is:
（-∞,2）∪（2+∞）

Is the domain the value range of X? Is the domain the value range of Y?

Strictly speaking, the domain is the value range of the independent variable, and the domain is the value range of the dependent variable. If a function expression has more than one independent variable, then there are two domains. Generally, if the function expression has only x and y, what you said is true

The domain of the function y = 2tan (x-pie / 3) is?

The solution comes from the problem
X - π / 3 belongs to (K π - π / 2, K π + π / 2) k belongs to Z,
That is, X belongs to (K π - π / 6, K π + 5 π / 6) and K belongs to Z
So the definition domain of function is (K π - π / 6, K π + 5 π / 6) k belongs to Z

The minimum positive period of the function y = 2tan (2x + π / 4) is the domain of definition?

Minimum positive period π / 2
Domain (- 3 / 8 π + K / 2 π, 1 / 8 π + K / 2 π) (K ∈ z)

Finding the minimum positive period sum domain of function y = 3tan (x / 2 - π / 3)

T=π/(1/2)=2π
x/2-π/3≠kπ+π/2
x/2≠kπ+5π/6
X ≠ 2K π + 5 π / 3, K is an integer

Finding the minimum positive period sum domain of function y = 3tan

T=π/(1/2)=2π
x/2-π/3≠kπ+π/2
x/2≠kπ+5π/6
X ≠ 2K π + 5 π / 3, K is an integer

Find the minimum positive period sum domain of function y = 3tan (x / 2-pai / 3)

T=2π
x/2-π/3≠kπ+π/2
x≠2kπ+5π/3
So the domain of definition is {x | x ≠ 2K π + 5 π / 3, K ∈ Z}

Given the domain {1,2,3,4} and the range {5,6,7}, how many ways can we find such a function?
If we know that the definition field of function f (x) is {1,4}, and the value field is {5,7}, then there are () such functions f (x).

Starting from the definition of function, first of all, an X corresponds to a Y in the definition field, which can only be 5.6.7 corresponding to three numbers in 1234 one by one, and then choose one corresponding from 567 for the remaining number in the definition field, that is, two numbers in 1234 correspond to the same Y
I don't know if you have learned the knowledge of permutation and combination, C4 = 2 * A33 = 36

The definition field and value field of function y = (1 / 7) ^ X are

The domain is from negative infinity to positive infinity
As for zero to positive infinity
The image of this function is a monotonic decreasing function through the point (0,1) in the coordinate system
You can draw this picture in the coordinate system

3x-2(x+1)=4-3(2x-5)

The solution is 3x-2 (x + 1) = 4-3 (2x-5)
We get 3x-2x-2 = 4-6x + 15
That is X-2 = 19-6x
That is 7x = 21
The solution is x = 3