It is known that y = f (x) is a monotone increasing function in its domain of definition, and its inverse function is y = 1 / {f (x)}, If ∣ 1 / F (x + 1) ∣ ≤ 3, then the value range of X is? (please give an explanation,)

If the inverse function of y = f (x) is y = 1 / {f (x)}, then x = 1 / {f (f (x))}, then 1 = 1 / {f (f (1))}, if the image of y = f (x + 1) passes a (- 4,0); B (2,5), then f (3) = 0, f (1) = 5, substituting f (1) = 5 into 1 = 1 / {f (f (1))}, then 1 = 1 / {f (5)}, f (5) = 1, considering f (1) = 5

Does y = f (x) have inverse function in monotone interval

The existence of inverse function means that there is a one-to-one correspondence between the independent variable and the variable in the "research interval", so the existence of inverse function should be in the "strictly monotone" interval. Monotone interval allows the existence of local and global constant functions, in this case, there is no inverse function

1. Monotone increasing interval of x ^ 2-2x-3 2. Inverse function of F (x) = X-1 / x + 1

Let f (x) = x ^ 2-2x-3, so a = 1, B = - 2, C = - 3
So - B / 2A = 1,
Because a is greater than 0, the monotone increasing interval of F (x) is (1, + ∞)
It's the same answer as the first person

Finding the monotone interval of function y = x ^ 2-2x + 3 and its inverse function on [- 2,1]

Y=(x-1)^+2
X ∈ [- OO, 1] decreasing function
X ∈ [1, + OO] increasing function
The inverse function is (X-2) + 1 x ∈ [2,3] under y = radical
(X-2) x ∈ [3,11] under y = 1-radical

The line passing through the origin intersects the image of function y = log 4 x at two points A.B. the line passing through point B intersects the image of function y = log 2 x at point C. if the line AC is parallel to the X axis, then the coordinates of point a are
A (1,0) B (4,1) C (radical 2,1 / 2) d (2,1)
My girlfriend is asking me

Exclude option a, (only one intersection)
C (not on y = log4x)
D (not on y = log4x)
Choose B
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Given the function y = 5x-3, find: (1) the coordinates of the intersection of the function image and x-axis, y-axis
(2) When x takes what value, the function value is positive, zero, negative

(0,-3) (3/5,0)
x>3/5 y>0
= =
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The coordinates of the intersection of the image and the X axis of the function y = - 5x + 2 are

（2/5,0）

What conditions must be satisfied to prove that a graph is centrosymmetric?

The following conditions should be met:
① The line of the corresponding point passes through the center of symmetry
② The line connecting the corresponding point and the center of symmetry is equal
If you have any questions, please ask; if you are satisfied, please adopt. Thank you!

Are two congruent figures centrosymmetric

How to prove that two figures are centrosymmetric or symmetric about a point

As long as two groups of corresponding points of the corresponding figure are connected respectively, it is proved that the two lines are equal, and then it can be said that this is a centrosymmetric figure

It is known that y = f (x) is a monotone increasing function in its domain of definition, and its inverse function is y = 1 / {f (x)}, If ∣ 1 / F (x + 1) ∣ ≤ 3, then the value range of X is? (please give an explanation,)