Question

Can someone please help me solve

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

im trying to find it's inverse

Answer 1

ok
is this your question??
\[\Large y=\frac{x-3}{2x+4}\]

Answer 2

Yes

Answer 3

ok
first of all replace all x with y's and all y's with x
\[\Large x=\frac{y-3}{2y+4}\]
is it ok with you ?

Answer 4

sure

Answer 5

now solve the above for y.
can you do this ?

Answer 6

That's were I get confused, I'm not sure on how to eliminate the format as a fraction

Answer 7

sorry openstudy crashed me :(
let me type again.

Answer 8

ok

Answer 9

ok
can i write this as
\[\Large x(2y+4)=y-3\]

?

Answer 10

sure, I did that. Then would I make it 2xy+4x = y-3?

Answer 11

yes

Answer 12

then divide the y out?

Answer 13

now can i take y to the left side and 4x to the right
\[\Large 2xy-y=-3-4x\]
it it ok with you ?

Answer 14

is*

Answer 15

sure

Answer 16

ok now taking y common from the left side
\[\Large \implies (2x-1)y=-3-4x\]
now ok ??

Answer 17

I'm sorry, I'm a bit confused

Answer 18

ok take common y from the following and tell me what you got
\[\Large 2xy-y=-3-4x\]

Answer 19

it would be (2x-1)y = -3-4x

Answer 20

yes exactly!

Answer 21

I know that I should try to get all my x's on one side, so I would I divide both sides by 2x-1

Answer 22

well done that's true !!!!!

Answer 23

Do I stop there, or continue?

Answer 24

Just one more step !!
after division by 2x-1 you get
\[\Large y=\frac{-3-4x}{2x-1}\]
agree?

Answer 25

Yes, If I continue to do so... I would get y = 3-2x?

Answer 26

I hope I'm not making my own math rules

Answer 27

I mean y = 3+2x

Answer 28

so now you have
\[\Large y=\frac{-3-4x}{2x-1}\]
just replace y with \[ f^{-1}(x)\]
and it is your answer
\[\Large \implies f^{-1}(x)=\frac{-3-4x}{2x-1}\]

Answer 29

ok, thanks. How would I graph that?

Answer 30

graphing is a whole different story !!!

Answer 31

just to give you hint

take different values of x .put in the above expression. you will get corresponding values of f^(-1)(x)
Plot x values on x axis and
f^-1(x) values on y axis.