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Why do we need to find the range of the original function when we find the inverse function of a function
The value range of the original function is the definition domain of the new function. Sometimes, it is difficult to see the definition domain after directly finding the inverse function
such as
Y = √ x defines the domain as X ≥ 0 and the range y ≥ 0
The inverse function is y = x
If you don't look at the value field first and look at this formula, the definition field should be x = R
So we must first find the value domain, that is, the domain of inverse function definition
Y = the inverse function of 25-4x ^ 2 under the root sign, As the title
y=√(25-4x²)
The range is [0,5]
y²=25-4x²
4x²=25-y²
x²=(25-y²)/4
x=√(25-y²)/2
So the inverse function is
y=√(25-x²)/2
The domain is defined as [0,5]
Inverse function 1. Y = x ^ 3 + 4 (x belongs to R) 2. Y = 1-2 / (x + 3) (x belongs to R and X is not equal to - 3) 3. Y = (4x + 1) / (5x-3) (x belongs to R and X is not equal to 3 / 5) 4. Y = inverse function of root 2X-4 {x > equal to 2}
Y = 1-2 / (x + 3) (x belongs to R and X is not equal to - 3) y = 2 / (1-x) - 3) (x belongs to R and X is not equal to - 3) y = 2 / (1-x) - 3) (x belongs to R and X is not equal to 1) 3. Y = (4x + 1) / (5x-3) (x belongs to R and X is not equal to 3 / 5) y = (3x + 1) / 4x-4) 4. Y = radical 2X-4 {x > equals 2} y = (x ^ 2 + 4) / 2 (x > = 0)
If 4x-7 = 5x-5, what is 3-x equal to
4x-7=5x-5
4x-5x=7-5
-x=2
x=-2
-x=2
3-x=2+3
3-x=5
What are positive functions and inverse functions
A positive proportional function is a function of the form y = KX, K is not equal to 0, y is a constant value
Inverse proportional function. Is xy = k, K is not equal to 0
Some views on the image of inverse function Y = f (x) and x = F-1 (y) are different functions, but their images are the same 2. X = F-1 (y) and y = F-1 (x) are the same functions, but their images are different Are these two statements correct I think it must be right. The person who refutes should give reasons give an example: For example, 2 corresponds to 4 and 1 respectively, but the images are the same, because the latter is derived from the former 2. Y = 3x ^ 2 and x = 3Y ^ 2, although the symbols of independent variables and dependent variables are opposite, the corresponding rules are the same, and they are the same functions. Their images are different
Both statements are correct
First, let's clarify the definition of functions
Let X be included in R, if there is a corresponding rule f from X to R, which is for every x ∈ x, there is a unique y ∈ r corresponding to x under the corresponding rule F, then this correspondence rule f is said to be a function on X (Science Press, Vol. 1, page 6-7)
In other words, a function is a corresponding rule between sets. Generally speaking, these sets are usually number sets. Combining with this problem, whether the two functions are the same or not depends on whether their corresponding rules are consistent or not
F and F-1 are two corresponding rules here, so f and F-1 in the first proposition are different, so they are not a function; in the second proposition, the correspondence methods are both F-1, so they are the same function
Because of inertia thinking, people usually think that x is an independent variable and Y is a function. In fact, this is just a habit. It depends on who is the original image of the mapping relationship determined by the corresponding law
As for the function image, the point on the horizontal axis is usually used to represent the coordinates of X, and the point on the vertical axis corresponds to the value of Y. when drawing the function image, the analytic formula of the function can be regarded as an equation about (x, y). It is just like the equation of ellipse and hyperbola. X and y are equal in status. When drawing the image, we don't need to consider who is the independent variable and who is the function, The value of X corresponds to the X axis, and the value of Y corresponds to the Y axis
Images of reciprocal functions
As for the symmetry of the line y = x, some of the intersection points of the images which are inverse functions of each other are on y = x and some are not
Does the inverse function of a function have an inverse function?
If the inverse function of F (x) is f (x), then the inverse function of F (x) is f (x), because the inverse function of function is the image of y = x as the symmetry axis, and the function symmetrical with the original function is the inverse function of the original function, then the symmetric function of the inverse function is of course the original function
Is inverse function a function? In my opinion, the inverse function becomes an inverse function whose W is not restricted under the condition that the D of the direct function remains unchanged. It is a set of numbers, which can be commented and explained by experts
A normal function may have "many to one" phenomenon, and vice versa is "one to many", which is meaningless. Therefore, in order to require that the reverse is also a function, the original function is required to be single, that is, different elements must have different results after being left and right by the function, It is mapped from the value range of the original function to its definition domain
Inverse function of y = INX + 1, (x > 0)
Y-1 = LNX, e ^ (Y-1) = x, inverse y = e ^ (x-1)
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- 14. 0
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