Question

I think my brain has vapor lock. I can't seem to solve for y. Please help

X=y/(y-1)

Answer 1

@precal

Answer 2

multiply both sides by (y-1)
as a first step

Answer 3

what do you get?

Answer 4

Oops it is supposed to be (y+1)

I get

X(y+1)=y

Answer 5

yes now distribute the x (multiply x* y and x*1)

Answer 6

Xy+1x=y

Answer 7

btw 1x is usually just written as x

Answer 8

then subtract y from both sides, and while you are at it, subtract x from both sides

Answer 9

This is where I am confused am I moving the single y over to the left so to speak?

Answer 10

And I thought you would have to dived both sides by x?

Answer 11

xy + x= y

you can do "the same thing" to both sides, and it stays equal:
xy + x -y = y - y

simplify y-y to be 0
xy + x -y =0

now do the same for x: subtract x from both sides

Answer 12

and yes, the reason for this is to "move" y to the left and x to the right side

Answer 13

After subtracting x from both sides

Xy-y=-x

Answer 14

now "factor out" y from the left side. This is the opposite of "distributing"

Answer 15

Y(x-1)=-x

Answer 16

now divide both sides by (x-1)

Answer 17

I guess then divide both sides by x-1?

Answer 18

Y=-x/(x-1)


But the book answer is

Y=x/(x-1)

Answer 19

yes. You have the correct answer, and I was going to point out one other thing.

\[ y= \frac{-x}{(x-1)} =\frac{-x}{(x-1)}\cdot \frac{-1}{-1} = \frac{x}{-(x-1)}= \frac{x}{1-x}\]

Answer 20

notice that -(x-1) is the same as -1*(x-1)
distribute the -1 to get -1*x + -1*-1 which is -x +1
rewrite -x+1 ast 1-x

Answer 21

if the book says x/(x-1) it looks like a typo somewheres....

Answer 22

I was originally trying to find the inverse of

F(x)=x/(x+1)

Answer 23

We can test your inverse.
pick x=3 (some arbitrary number)
F(x)= F(3)= 3/4

if we call the inverse of F(x) G
then G(3/4) should give back 3

G(x) = -x/(x-1)
G(3/4)= -3/4 / (3/4-4/4) = -3/4 / -1/4 = 3
so it works.

Answer 24

The graph of my answer does not look like the graph of the book answer. And I never could find three points (whole numbers) to verify. I only found two but they work with both my answer and the book.

Answer 25

do they graph the original function? if the original function was F(x)= x/(x-1) then its inverse would be G(x)= x/(x-1)

Answer 26

Original function

F(x)=x/(x+1)

I graphed it using a TI

Answer 27

Here is F(x)= x/(x-1) as a comparison
http://www.wolframalpha.com/input/?i=inverse+F%28x%29%3D++x%2F%28x-1%29+


and here is F(x)= x/(x+1)
http://www.wolframalpha.com/input/?i=inverse+F%28x%29%3D++x%2F%28x%2B1%29+