How do I find the inverse of f(x) = (4x+9)/(2x-3)?

[Ry122]

how do i find
f(x)^-1 of y=4x+9/2x-3
the answer in the back of the textbook is

f(x)^-1=3x+9/2x-4

 

[christianjb]

Show your attempt at a solution, or pay me 1 dollar for doing your homework for you (your choice).

 

[Ry122]

2x=4x+9/y + 3y/y
2x=4x+9+3y/y
How do i move 4x to the other side?

 

[christianjb]

is 9/2x in your original post 9/(2x)? Just want to check.

 

[Ry122]

Heres the full working out:
y(2x-3)=4x+9
2x-3=4x+9/y
2x=4x+9/y + 3
2x=4x+9/y + 3y/y

 

[christianjb]

You got to learn to put brackets in your eqns. There's no way anyone could have understood your original problem without the brackets.

y(2x-3)=4x+9
x(2y-4)-3y=9
x=(9+3y)/(2y-4)

 

[Ry122]

Sorry to bother u again but how
do u get from
y(2x-3)=4x+9 to
x(2y-4)-3y=9

 

[christianjb]

expand and collect terms in x

y(2x-3)=4x+9
->
y2x-3y=4x+9
->
x(2y)-3y=x(4)+9
->
x(2y-4)-3y=9