how do you find the inverse of (x+1)/(x+2)?

Question

please show work thanks.

Answer 1

So, what you have to do is to let f(x) = (x+1)/(x+2).
since we know that y=f(x),
y = (x+1)/(x+2). a rule of inverse functions is interchanging x and y and then solve for y. so interchanging x and y,
x = (y+1)/(y+2). multiplying both sides by y+2,
x(y+2) = y+1.
xy +2x = y+1. To solve for y, we have to group the terms with a variable. So, we have:
xy - y = 1 - 2x
y(x -1) = 1-2x. dividing both sides by x-1 to isolate y,
y = (1-2x)/(x-1). thus, this is now the inverse function. this is denoted by f -1(x).
So, f-1(x) = (1-2x)/(x-1)

Answer 2

Inverse: Flip the top and bottom. Example inverse of 1/2 is 2/1 or the inverse of 12/5 is 5/12. Got it?

Answer 3

Suppose y = f(x) = (x+1)/(x+2). We need to know what x is. So we solve:

(x+2)y = x+1
yx+2y = x+1
yx-x = 1-2y
(y-1)x = 1-2y
x = (1-2y)/(y-1)

Therefore f⁻¹(x) = (1-2x)/(x-1) (just replace the ys with xs).

Answer 4

y=(x+1)/(x+2)
to find the inverse of this function interchange x and y
x=(y+1)/(y+2)
x(y+2)=y+1
xy+2x=y+1
xy-y=1-2x
y(x-1)=(1-2x)
y=(1-2x)/(x-1)