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Value range y = 5x-1 / 4x + 2! I have worked out the whole process. The main reason is why 7 / (8x + 4) ≠ 0?
Because 4x + 2 is the denominator in the original formula, it can not be zero; therefore, 8x + 4 can not be zero, the numerator is not zero, and the denominator is not zero; therefore, the whole formula is not equal to zero
The inverse function of y = 4x + 1 / 5x-3, As the title
y=(4x+1)/(5x-3)
5xy-3y=4x+1
5xy-4x=3y+1
(5y-4)x=3y+1
x=(3y+1)/(5y-4)
The inverse function y = (3x + 1) / (5x-4)
Y = (4x + 1) / (5x-3) (x belongs to R, and X is not equal to 3 / 5
y=(4x+1)/(5x-3)
y(5x+3)=4x+1
5yx+3y=4x+1
(5y-4)x=1-3y
x=(1-3y)/(5y-4)
x. The inverse function is y = (1-3x) / (5x-4) (x is not equal to 4 / 5)
What is the inverse function
In general, if x corresponds to y with respect to a corresponding relation f (x), y = f (x). Then the inverse function of y = f (x) is y = F-1 (x)
The condition for the existence of inverse function is that the original function must be one-to-one corresponding (not necessarily in the whole number field)
[properties of inverse function]
(1) The images of two functions which are reciprocal functions are symmetric with respect to the straight line y = X;
(2) The necessary and sufficient condition for the existence of inverse function is that the function is monotone in its definition domain;
(3) The monotonicity of a function is consistent with its inverse function in the corresponding interval;
(4) There must be no inverse function for even function, and no inverse function for odd function. If an inverse function exists for an odd function, its inverse function is also an odd function
(5) All implicit functions have inverse functions;
(6) The consistency of the monotone function in a interval is consistent;
(7) Strictly increasing (decreasing) function must have inverse function [existence theorem of inverse function]
(8) Inverse functions are mutual
(9) The opposite of definition domain and range is opposite to each other
(10) Not all functions have inverse functions such as y = x to the even power
Example: the inverse function of y = 2x-1 is y = 0.5x + 0.5
The inverse function of y = 2 ^ x is y = log2 X
Example: finding the inverse function of function 3x-2
The definition domain of y = 3x-2 is R and the range of value is r
From the solution of y = 3x-2
x=1/3(y+2)
If x and y are interchanged, then the inverse function of y = 3x-2 is
y=1/3(x+2)
Application of inverse function For example: let y = f (x) have an inverse function, y = F-1 (x), and y = f (x + 2) and y = F-1 (x-1) are reciprocal functions, then the values of F-1 (2004) - F-1 (1) are: A.4008 B.4006 C.2004 D.2003
Y = f (x + 2) and y = F-1 (x-1) are inverse functions of each other,
And y = f (x + 2) and y = F-1 (x) - 2 are reciprocal functions,
So F-1 (x-1) = F-1 (x) - 2,
That is, F-1 (x) - F-1 (x-1) = 2,
So F-1 (2004) - F-1 (1) = 4006
Answer B
Application of inverse function If and only if the function y = x? - 2ax-3 has an inverse function on the interval [1,2] A.a∈（-∞,1] B.a∈[2,+∞) C.a∈[1,2] D.a∈（-∞,1]∪[2,+∞) Is the interval [1,2] x or Y
[1,2] is the range of X
If there is an inverse function, it is monotonic
So the axis of symmetry x = a is not in [1,2]
So a < = 1, a > = 2
Choose D
What are the properties of inverse function and original function?
1. The inverse function of a function is symmetric to the image of the original function with respect to the straight line y = X;
2. The domain of the original function is the range of its inverse function, and the domain of the original function is the domain of its inverse function
What is an inverse function? What is an inverse function,
Generally speaking, if the corresponding F of the function y = f (x) is one-to-one correspondence from the definition domain to the range of value of the function, then the function determined by the "inverse" correspondence of F-1 is called the inverse function of the function. The definition domain and range of the inverse function x = F-1 (x) are the range and range of the function y = f (x)
Ask a question about the properties of function and inverse function Why (x) > 1=
It's mainly about symbols
Any given y = f (x), X belongs to the definition domain D, and Y belongs to the range Z
There is an original function x = g (y), y belongs to the range Z
So x = g (y),
Substituting Y > x, that is, Y > G (y), where y belongs to the range Z
Since y is any value in Z, we can also use another symbol x, which is
X>G(X),
The reason you may not understand is that the first X belongs to set D and the last x belongs to set Z!
Inverse function property problem, determine inverse function The condition for the existence of inverse function: for any x1, X2 belongs to D, X1 is not equal to X2, there is f (x1) is not equal to f (x2). F establishes a one-to-one correspondence between D and y Y = x ^ 2, X belongs to R and has no inverse function Then y = cosx, X belongs to R. when y is taken as 1, X has many values corresponding to each other. Why does this function have an inverse function? The definition of inverse function is not one-to-one corresponding?
Y = arccosx is the inverse function of y = cosx, X ∈ [0, π]
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