What is the inverse function of the function y 2x 1?

Solution: Defined domain of y=2x+1.

is r, and the range is r

From y=2x+1, we get x=(y-1).

Swap x and y, then the inverse of y=2x+1 is obtained.

Be. y=（x-1）/2

What was said upstairs seemed to be good.

My understanding: the function y=2x+1

is represented by x y; (y is equal to how much x).

The inverse function is.

x is represented by y. (solve, x is equal to how much y) at the end. Use.

x and. Replace each other with y.

The inverse of the function y=2x+1 is y=(x-1) 2.

by y=2x+1

Get x=(y-1) 2

So the inverse of the original function is y=(x-1) 2.

Knowledge points: In general, let the range of the function y=f(x)(x a) be c, if you find a function g(y) where g(y) is equal to x, then the function x=

g(y)(y c) is called the inverse of the function y=f(x)(x a) and is denoted as y=f (-1)(x).

The inverse function y=f

x) and the domain are the domain and domain of the function y=f(x), respectively.

In general, if x corresponds to y with respect to some correspondence f(x), y=f(x), then the inverse function of y=f(x) is x=f

1(y)。The condition for the existence of an inverse function (a single-valued function by default) is that the original function must be one-to-one (not necessarily within the entire number field). Note: Superscript"−1"It doesn't mean power.

In calculus, f

n)(x) is used to refer to the nth differential of f.

If a function has an inverse function, the function is called invertible.

To put it simply, it is to swap y and x, for example, the inverse function of y=x+2 first uses y to represent x, that is, x=y-2, just change the positions of x and y, then y=x+2 inverse function is y=x-2.

It reads as follows:y=2x-1。

2x=y+1。

x=（y+1）/2。

So it's the inverse function.

is y=(x+1) 2=x 2+1 2.

Definition: Nakai nucleus.

In general, let the function y=f(x)(x a) be in the range of values.

is c, according to the relationship between x and y in this function, x is represented by y, and x= g(y)If for any value of y in the inverse function of c, by x= g(y), x has a unique value in a that corresponds to it, then, x= g(y) means that y is the independent variable and x is the function of the dependent variable y, and such a function x= g(y)(y c) is called the inverse function of the function y=f(x)(x a), which is denoted as the domain of y=f (-1) (x) inverse function y=f (-1) (x).

The value range is the hole value range and the definition domain of the function y=f(x).

The inverse of the function y=2x+1 is y=1 2x-1 2y=2x+1

2x=y-1

x=1/2y-1/2

So y=1 2x-1 2

y=2x-1

y+1=2x

x=y/2+1/2

y=x/2+1/2

is the inverse function of y=2x-1.

y = 1/x

x is not equal to 0

Solution: y=2x+1

x+1=log2y

i.e. x=log2y-1

Therefore, the inverse function of y=2x+1 is y=log2x-1, so the answer is: y=log2x-1(x 0).

y-1=2x rock beat(1+2x)-1=-1 (1+2x)1+2x=-1 (y-1).

2x=-1/(y-1)-1=-y/(y-1)x=-y/(2y-2)

The inverse function of the Xun Zao Bridge is y=-x (2x-2), and x is not equal to 1

Problem solving idea: from y 1 2 x 1+ 2 x, take y as a constant, find the imitation of x log 2 1 y 1+y, and then x,y are swapped, and the inverse function of the function y 1 2 x 1+ 2 x is y sell volt log 2 1 x 1+x ,x (-1,1).

y=1-2x

1+2x,y+y 2x=1-2x,y+1) 2x=1-y,2x=1-y1+y,x=log2

1-y1+y,x,y are swapped to get the function y=

The inverse function of 1-2x1+2x is y=log2

1-x1+x，x∈（-1，1）．

So the answer is: y=log2

1-x1+x，x∈（-1，1）．10,

y=x^2+2x-1

y=(x+1)^2-2

x+1)^2=y+2

x+1=√(y+2)

x=√(y+2)-1

The counter-letter knows that Zheng Shu is y= (x+2)-1 before the nuclear Song

y=x-2 x+1, the answer is as high as (x+1)y=x-2 at this time, x≠-1 gives xy+y=x-2

i.e. y+2=(1-y)x

i.e. x=(y+2) (1-y).

In other words, the inverse function of this group lifting with collapsed reed function is.

y=(x+2) (1-x) where x≠1

Untie. y=2^x-1

The value range is: y> lift bend 1

y+1=2^x

x=log2(y+1)

Inverse functions. Answer for the noise: y=log2(x+1)(x>1).