It is known that the inverse function of the function f (x) = log2x (x > 0) is g (x), and there is g (a) g (b) = 8. If a < B, a > 0, then 1 A+4 The minimum value of B is______ .

The inverse function of the function f (x) = log2x (x > 0) is g (x),
∴g（x）=2x，
G (a) g (b) = 8
A + B = 3, and a < B, a > 0
∴1
A+4
b=（1
A+4
b）（a+b）×1
3=1
3（5+b
a+4a
b）≥1
3 (5 + 4) = 3, if and only if B
a＝4a
The equal sign is established,
Then 1
A+4
The minimum value of B is 3
So the answer is 3

Given that the function f (x) = log2x (2 is the base), X ∈ [2,8], the minimum value of the function g (x) = f ^ 2 (x) - 2AF (x) + 3 is h (a)

∵f(x)=log2x,x∈[2,8]
∴f(x)∈[1,3]
g(x)=(f(x))^2-2af(x)+3+a^2-a^2
=(f (x) - a) ^ 2 + 3-A ^ 2 symmetry axis X = a, opening up
When A3, H (a) = 3 ^ 2-2a × 3 + 3 = 12-2a
It means to change yuan

Given that f (x-1) = x2-2x + 3 (x ≤ 0), find the inverse function of F (x), and write the definition and range of the inverse function As the title

Given that f (x-1) = x2-2x + 3 (x ≤ 0), find the inverse function of F (x), and write the definition and range of the inverse function
Analysis: let t = X-1, t

The value range of the function y = 2x-1 / x + 1 (1 ≤ x ≤ 4) is expressed in inverse representation (or inverse function method),

y=2x-1/x+1=2+（-3/x+1）
1≤x≤4
2≤x+1≤5
-3/2≤-3/x+1≤-3/5
1/2≤2+（-3/x+1）≤7/5
The value is [1,2]

Find the inverse function of y = 2x + 1 / x + 1, and find the definition and range of inverse function Given that the function y = x + radical X-1 has inverse function, find the range of inverse function

1. The inverse function is y = 1-x / X-2, and the definition domain is x not equal to 2, and the range of value is not equal to - 1. 2. The range of inverse function is the domain of original function, that is, X-1 > 0, x > 1

Y = 5x-1 / 4x + 2 using inverse function method

This method is to solve x, express x with y, and then look at the definition domain of Y, which is the value range of the original function. Y = (5x-1) / (4x + 2) y (4x + 2) = 5x-14xy + 2Y = 5x-14xy-5x = - 2y-1x = (- 2y-1) / (4y-5), we can see that y ≠ 5 / 4. Therefore, the range of original function is: (- ∞, 5 / 4) ∪ (5 / 4, + ∞)

Y = 5x-1 / 4x + 2

y=(5x-1)／(4x+2)
=(5x+5/2-7/2)/(4x+2)
=(5x+5/2)/(4x+2)-7/[2(4x+2)]
=5/4-7/(8x+4)
Because 7 / (8x + 4) is not equal to 0,
Y = 5 / 4-7 / (8x + 4) is not equal to 5 / 4
therefore
The range of y = (5x-1) / 4x + 2 is y, not equal to 5 / 4

Y = 4x + 1 / 5x-3, inverse function?

Y=（4X+1）/（5X-3）
5yx-3y=4x+1
（5y-4）x=3y+1
x=（3y+1）/（5y-4）
So the inverse function is
y=（3x+1）/(5x-4)（x≠4/5）

What is the inverse function

In general, let the value range of the function y = f (x) (x ∈ a) be c. according to the relationship between X and Y in this function, X is expressed by Y, and x = f (y) is obtained. If any value of Y in C, by x = f (y), X has a unique value corresponding to it, then x = f (y) means that y is an independent variable and X is a function of dependent variable y

What is inverse function~ The inverse function of y = f (x) is x = f (- 1) (y). In order to express conveniently, X and y are changed to y = f (- 1) X. so, x = f (- 1) (y) and y = f (- 1) x are inverse functions of the original function. Which is it

Both of them are inverse functions of the original function, but the two independent variables are different. Of course, if we put them in the same coordinate system, x = F_ Y and function itself are actually the same function, but their independent variables are not the same

It is known that the inverse function of the function f (x) = log2x (x > 0) is g (x), and there is g (a) g (b) = 8. If a < B, a > 0, then 1 A+4 The minimum value of B is______ .