Question

inverse functions really stump me.
Let g(x)= 2x-3/x-1
determine g inverse(x)

Answer 1

http://en.wikipedia.org/wiki/Slice_(soft_drink) slice this is for you lol

Answer 2

ok now i'm gonna find inverse no more lol

Answer 3

let g(x) = y

Answer 4

yx - y = 2x - 3

-y + 3 = x ( 2 -y)

x = 3 - y
-----
2 - y

Answer 5

hence inverse is
3 -x
g(x) = --------
2 - x

Answer 6

thanks for the slice info.

Answer 7

anytime

Answer 8

so i got y= -3-x
--------
x-2

Answer 9

did i do something wrong?

Answer 10

Looks not quite right. What were your steps? I'll try to find the problem.

Answer 11

So i started out with g(x) = 2x-3
-----
x+1

I then did x= 2y-3
------
y+1
x(y+1)=2y-3

x(y+1) -2y = -3

xy + x - 2y = -3

xy - 2y = -3 - x

y(x-2) = -3-x

y= -3-x
---------
x-2

Answer 12

I thought the original problem was (2x-3)/(x-1). You now have (x+1) in the denominator.
What you did does look good, for this new problem!

Answer 13

ah yes i did put it as x-1 but the problem should be x+1. thank you

Answer 14

BTW, if this is multiple choice, they might list the solution as
(x+3)/(2-x) which you get by multiplying the top and bottom by -1

Answer 15

so another question. O got the domain as x can not equal 1. Would that be correct?

Answer 16

never multiple choice I have to show my work

Answer 17

The domain of g(x) are all the x's that give you a valid answer.
g(x)= (2x-3)/(x+1)

What happens when x= -1?
(2*-1 -3)/(-1+1) = -5/0
oops! dividing by zero is very very bad. So the domain of g(x) must exclude -1