Find the inverse function y = x / (x + 2)

y=x/(x+2)
y(x+2)=x
xy+2y=x
x-xy=2y
(1-y)x=2y
x=2y/(1-y)
The inverse function is
y=2x/(1-x)

Answers to 3 and 6 questions on 24 pages

The first and the third are all about the first order function. The image is a straight line (two points can be arbitrarily determined, then the corresponding line), the definition and range are all real numbers; the second is the inverse proportional function, the image is in the first three quadrants of the double

It is known that an is an arithmetic sequence and A3 = - 6 A6 = 0 Find the general term an 2 if the arithmetic sequence BN satisfies B1 = - 8, B2 = a1 + A2 + a3, find the sum formula of the first n terms of BN

One
Let the first term be a and the tolerance D
a3=a+2d=-6
a6=a+5d=0
The solution is as follows:
a=-10
D=2
an=-10+2(n-1)=-10+2n-2=2n-12
Two
b1=-8
b2=a1+a2+a3
=(2-12)+(2*2-12)+(2*3-12)
=-10-8-6
=-24
The tolerance is b2-b1 = - 24 - (- 8) = - 16
bn=-8+（-16）（n-1）
=-8-16n+16
=8-16n
Sum of the first n items
S(bn)=(b1+bn)*n/2
=(-8+8-16n)*n/2
=-8n^2

Senior one mathematics senior one mathematics please answer in detail, thank you! (22 15:43:15) When to use and to connect two intervals, and when to connect two intervals with ∪?

The relationship between intersection and set
Define domain, connect with 1 & 2, represent the set of 1 and 2, that is, all the fields in 1 and 2 add up
1 u 2, which represents the intersection of 1 and 2, is the common domain of 1 and 2
In short, set is all, intersection is common

If the function f (x) = ax − 1 Ax + 1 (a > 0 and a ≠ 1) (1) Judge the parity of F (x); (2) When a > 1, the monotonicity of F (x) on (- ∞, + ∞) is determined and proved

(1) From the definition domain of F (x) is (- ∞, + ∞), symmetric about the number 0 (2 points) f (− x) = a − x − 1a − x + 1 = 1 − ax1 + AX = − f (x), it is concluded that ﹣ f (x) is an odd function on R. (6 points) (2) when a > 1, f (x) increases monotonically on (- ∞, + ∞). (8 points) (no points are deducted this time

[1 - (sin160 °) ^ 2] A. Cos160 B. - cos160 C. soil cos160 D. cannot be determined

B
Because (sin160 °) ^ 2 + (cos160 °) ^ 2 = 1
Therefore, 1 - (sin160 °) ^ 2 = (cos160 °) ^ 2
Under root sign (cos160 °) ^ 2 = | (cos160 °)|
Since cos160 is less than 0, the absolute value is followed by - cos160

Senior one mathematics (about inverse function) Find the function f (x) = {x ^ 2 + 1 (x = - 1) Inverse function of

f(x)={x^2+1 (x=-1)
The solution is f (x) = {- √ (x-1) (x ≥ 2)
f(x)={1-x (x＜2)

Finding the inverse function of y = 1 + ln (x + 2) and its definition domain

Firstly, the definition domain of the original function is: (- 2, positive infinity)
The value range of the original function is: R
y-1=ln(x+2)
e^(y-1)=x+2
x=e^(y-1)-2
The inverse function is: y = e ^ (x-1) - 2. The definition domain of inverse function is R and the range of value is (- 2, positive infinity)

The inverse function of y = ln (x + 1) is? Its domain is? It mainly defines the domain. Give the following reasons

Inverse function: x = e ^ Y-1
Definition domain: y belongs to negative infinity to positive infinity. Because the value range of function y = ln (x + 1) is from negative infinity to positive infinity, that is, y belongs to negative infinity to positive infinity, so the definition domain of inverse function also belongs to negative infinity to positive infinity

Solving an inverse function and its domain y = ln (x + sqrt (x.x + 1))

Let t = x + sqrt (x ^ 2 + 1)
Because sqrt (x ^ 2 + 1) > X: is always positive
:. The domain is (- OO, + OO)
T increases monotonically in X ∈ R (because g (x) = x, H (x) = sqrt (x ^ 2 + 1) monotonically increases
The range of Y is (- OO, + OO)
x+sqrt(x^2+1)=e^y =>x=e^y-1/e^y (y∈R*)
Then the inverse function is y = 1 / 2 (e ^ X-1 / e ^ x) (x ∈ R *)

Find the inverse function y = x / (x + 2)