Mathematical problems_ Inverse function It is known that f '(x) is the inverse function of F (x) Then find the inverse function of F (2x-1) (expressed by F '(x))

Let (y) = 2x - 1) + (f) denote (f) 2x - 1 '+ 1
By exchanging X and y, we get the inverse function y = (f '(x) + 1) / 2

If the function y = f (x) is the inverse function of the function y = ax (a > 0 and a ≠ 1), its image passes through a point（ a. A), then f (x) =___ .

Let X be the inverse function of x = X（
a，a），
∴a=loga
a. That is, a = 1
2，
So the answer is: Log1
2x．

Math problem ~ about inverse function, thank you How to find the inverse function? Y=1+LG（X+2） Please let me know the detailed process. Thank you very much

lg(X+2)=y-1
So:
x+2=10^(y-1)
x=10^(y-1)-2
So the inverse function is:
y=10^(x-1)-2

Solving inverse function y=1-3x/5x-2 y(5x-2)=1-3x (5Y + 3) x = 1 + 2Y why does 5x-2 change y + 3 x=(1+2y)/(5y+3) Inverse function: y = (1 + 2x) / (5x + 3)

By y = (1-3x) / (5x-2),
The results show that y (5x-2) = 1-3x,
5xy-2y+3x=1,
5xy+3x=1+2y,
（5y+3）x=1+2y
x=(1+2y)/(5y+3)（1）
∴y=（1+2x）/（5x+3）.（2),
(1) Let X be a function of Y,
(2) The inverse function of the original function is obtained by exchanging X and y
Your steps are all right

Finding inverse function in mathematical problems f(sinx)=cos2x+1, Find f (cosx) 2-2(cosX)^2 =1-cos2x How did it change

According to the formula
cos2x=1-2(sinx)^2
therefore
f(sinx)=2-2(sinx)^2
Then f (x) = 2-2x ^ 2
Substitution
f(cosx)=2-2(cosX)^2
We can simplify it again

Ask for help of inverse function mathematics problem f(x)=ln(9+4x)+ln(9x-2) Analytic expression of inverse function

F (x) = ln (9 + 4x) + ln (9x-2) = ln [(9 + 4x) (9x-2)] in (f (x)) = in {ln [(9 + 4x) (9x-2)]} = (9 + 4x) (9x-2) = 36x ^ 2 + 73x-18 = (6x + 73 / 12) ^ 2-18 - (73 / 12) ^ 2. The analytic expression of the inverse function is x = {[in (f (x)) + 18 + (73 / 12) ^ 2] ^ (1 / 2) - 73 / 12} / 6

The function y = ax + B is the same function as its inverse function

y=ax+b
ax=y-b
x=y/a-b/a
Because the function y = ax + B is the same as its inverse function
therefore
a=1/a,b=-b/a
When a = 1, B = 0
When a = - 1, B is an arbitrary number

Given that the function FX = x ^ 2-4x-5, X belongs to [1,3], judge whether there is an inverse function? If there is an inverse function, why not?

non-existent
The value range of this function is [- 8, - 5] except y = - 5, a y value corresponds to two X values
In other words, one X corresponds to two Y values
This is not a function (the definition of a function)

Inverse function of y = 3sinx / 2, X ∈ [- π, π]

y=3sinx/2
x∈[-π,π]
y∈[-3,3]
sinx/2=y/3
x/2=arcsiny/3
x=2arcsiny/3
The inverse function of y = 3sinx / 2, X ∈ [- π, π] is y = 2arcsinx / 3x ∈ [- 3,3]

Let the complete set u = {1,2,3,4,5,6}, and set a and B are subsets of u. if a ∩ B = {1,3,5}, then a and B are called "ideal matching sets", which are recorded as [a, b]. How many such "ideal matching sets" [a, b] are there?

A∩B={1,3,5}, U={1,2,3,4,5,6}
It shows that 2,4,6 can only appear in a or B or AB, but not in three cases
ν there are three options for each of 2, 4 and 6
There are 3 * 3 * 3 = 27 possibilities

Mathematical problems_ Inverse function It is known that f '(x) is the inverse function of F (x) Then find the inverse function of F (2x-1) (expressed by F '(x))