If f (x) = (2x + 3) / (4x + 3) (x ∈ R and ≠ - 3 / 4), then f ^ - 1 (2) =? If wrong, please answer

If f (x) = (2x + 3) / (4x + 3) (x ∈ R and ≠ - 3 / 4), then f ^ - 1 (2) =? If wrong, please answer

The independent variable of the inverse function is the function value of the original function
f(x)=2
(2x+3)/(4x+3)=2
2x+3=8x+6
x=-1/2
So f ^ - 1 (2) = - 1 / 2

It is known that the function f (x) has an inverse function on the definition R, and f (9) = 18. If the inverse function of y = f (x + 1) is y = f ~ (x + 1), then f (2008) =? ∵ y = f ˉ (x + 1) ᙽ x + 1 = f (y), that is, y = f (x) - 1  f (x + 1) = f (x) - 1 how to get y = f (x) - 1

In X + 1 = f (y), change the letter X into the letter Y, and change the letter Y into the letter X to get: y + 1 = f (x), that is, y = f (x) - 1

It is known that the function y = f (x) defined on R has an inverse function y = f ^ - 1 (x), if the inverse function of function y = f (x + 1) is y = f ^ - 1（ If the inverse function is y = f ^ - 1 (x-1), and f (0) = 1, then f (12) =?

The inverse function y = f ^ - 1 (x-1) means that f (x) = Y-1
So y = f (x + 1) = f (x) + 1,
If x is a positive integer
f(x+1)=f(x)+1=f(x-1)+2=.=f(0)+x+1
So f (12) = 13

Finding the inverse function of function y = x + 1

x=y-1
Inverse function: y = X-1

The inverse function of the function y = 2x (x ≥ 1) is___ .

∵ when x ≥ 1, y = 2x ≥ 2,
The value range of the function y = 2x (x ≥ 1) is [2, + ∞),
If y = 2x is converted into logarithm, x = log2y can be obtained,
The inverse function of the original function is: y = log2x, (x ≥ 2)
So the answer is: y = log2x, (x ≥ 2)

0

y=1+In(x-1)
y-1=ln(x-1)
x-1=e^(y-1)
x=1+e^(y-1)
Change X and y
The inverse function is y = 1 + e ^ (x-1), (x ∈ R)

Given the image crossing point (1,4) of the function y = a ^ x + B, and the image crossing point (2,0) of its inverse function, the values of a and B are obtained

If the function y = a ^ x + B crosses the point (1,4), then a + B = 4
If the image of the inverse function crosses the point (2,0), then the original function passes through (0,2), so 1 + B = 2, so B = 1, a = 3

If we know the image crossing point (4, - 2) of the inverse function of the function f (x) = a ^ x (a > 0 and a ≠ 1), then the value of function a is

If the image of the inverse function is over (4, - 2), then the original function is over (- 2,4),
So a ^ 2 = 1 / 4, so a = 1 / 2

If the image of the inverse function of the function y = ax crosses the point (9,2), then the value of a is______ .

The point (9,2) is on the graph of the inverse function of the function y = ax,
Then point (2,9) is on the graph of function y = ax
Replace x = 2, y = 9 into y = ax,
9 = A2
The solution is a = 3
So the answer is: 3

It is known that the function y = f (x) and y = e ^ X are inverse functions. The image of the function y = g (x) and the image of y = f (x) are symmetric about the x-axis. If G (a) = 1, then the real number a value is

It is known that f (x) = LNX
g(x)=-ln(x)
Because g (a) = 1, ln (a) = - 1
That is, a = e ^ (- 1) (i.e. a = 1 / E)