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

find the inverse of the function

Question

y = (-3)/(x+4)

find the inverse of the function

anonymous · Answer

@Nnesha

xapproachesinfinity · Answer

do you have any ideas how to start?

xapproachesinfinity · Answer

what did you do in class?

anonymous · Answer

not really

xapproachesinfinity · Answer

nothing at all

xapproachesinfinity · Answer

don't remember what you did in class?

anonymous · Answer

No I meant I don't really know how to start off, that's what I'm trying to figure out

anonymous · Answer

is there a formula for it?

xapproachesinfinity · Answer

well im asking tell me anything you learned from class

xapproachesinfinity · Answer

about this

anonymous · Answer

Oh well I dunno much about this really I just started the section about finding inverse functions

xapproachesinfinity · Answer

well what did you start with in class
there is no way your teacher/prof would assign you this if nothing is done in the class

xapproachesinfinity · Answer

in order for me to help i need to know what you know and what you don't

anonymous · Answer

ok well I just got done doing something like this f(x) = x -3 and g(x) = x-5) find f(g(5))

xapproachesinfinity · Answer

Okay i will assume you don't know anything yet about inverses!

anonymous · Answer

That is what I said above

anonymous · Answer

@Nnesha

xapproachesinfinity · Answer

so what is an inverse function
basically and inverse it the operation we apply to undo some operation
say we have 5+(3)=8 to  undo addition we take 8-3=5
i started with 5 added 3 to get outcome 8
the inverse of that is start with 8 subtract 3 to get back to 5
more formally if have y=x-3 the inverse is x=y+3 then i just do a trick and switch the variable x and y so y=x+3

anonymous · Answer

oh okay

anonymous · Answer

so mine would be like x = (4y - 3)/(y)?

xapproachesinfinity · Answer

no just follow...

xapproachesinfinity · Answer

now i have y=4/(x-1)
so according to what i just did
1/4 y=1/(x-1)

xapproachesinfinity · Answer

then i flip the fractions
i get 4/y =x-1 yes?

xapproachesinfinity · Answer

i did error in the previous one so pay attention to this one carefully

xapproachesinfinity · Answer

once we solve this one you should do the same to solve yours

anonymous · Answer

ok...

xapproachesinfinity · Answer

$\huge y=\frac{4}{x-1}$ this is our function okay

anonymous · Answer

ok

xapproachesinfinity · Answer

first:
multiply by 1/4 both sides
$\huge \frac{1}{4}y=\frac{1}{4}\frac{4}{x-1}$

xapproachesinfinity · Answer

following...

xapproachesinfinity · Answer

so far okay?

anonymous · Answer

I think so

xapproachesinfinity · Answer

so i get $\huge \frac{1}{4}y=\frac{1}{x-1}$ 4 canceled out (4/4=1)

xapproachesinfinity · Answer

now flip the fraction
$\huge \frac{4}{y}=\frac{x-1}{1}$

xapproachesinfinity · Answer

good!

xapproachesinfinity · Answer

??

xapproachesinfinity · Answer

answer say no, yes say at least something

anonymous · Answer

lol I'm thinking

xapproachesinfinity · Answer

okay

anonymous · Answer

it looks okay I think...

xapproachesinfinity · Answer

make sure
not just okay hehe

xapproachesinfinity · Answer

make sure you got it lol

anonymous · Answer

I think I got it

xapproachesinfinity · Answer

okay

anonymous · Answer

so for mine I have to multiply both sides by 4/3

xapproachesinfinity · Answer

x-1/1 is just x-1 dividing by 1 does not change anything
so i get $\huge \frac{4}{y}=x-1$

xapproachesinfinity · Answer

no by -1/3 to cancel -3 on top of the left part fraction

xapproachesinfinity · Answer

why 4/3?

xapproachesinfinity · Answer

this needs some good algebra you know

anonymous · Answer

cause I thought you were flipping the denominator with the numerator and then multiplying both sides by it

xapproachesinfinity · Answer

i first multiplied to cancel
then i flipped the both sides fractions so the equality stays correct

xapproachesinfinity · Answer

if i had 1/y=x/2 flipping would give me y=2/x yes

xapproachesinfinity · Answer

that's what i did to that fraction

anonymous · Answer

oh ok

anonymous · Answer

okay so multiply both sides by -1/3 and then I'll get

xapproachesinfinity · Answer

back to our problem we are at $\huge \frac{4}{y}=x-1$
now i just need to add 1 to both sides to get $\huge \frac{4}{y}+1=x$
then i switch x and y to get 
$\huge \frac{4}{x}+1=y$

anonymous · Answer

oh ok.

xapproachesinfinity · Answer

once you multiply you cancel -3 on top
you get -1/3 y=1/(x+4)

xapproachesinfinity · Answer

the one i just solved got me to
$\huge y=\frac{4}{x}+1$ this the inverse i was looking for for my case

xapproachesinfinity · Answer

you follow the same steps to get there

anonymous · Answer

*bangs head against wall* I might have missed something from the last chapter this seems so convoluted

xapproachesinfinity · Answer

well one thing you can't go straight solving problems  without looking at you notes first

xapproachesinfinity · Answer

it does not work that way

xapproachesinfinity · Answer

yo need to study you notes and texbook before tackling any problem

anonymous · Answer

yea, I think I'm going back to my notes and try re-teaching myself some of this stuff and then I'll just use the stuff you've written as a reference for things

anonymous · Answer

anyrate I thank you for the work you've done. not many people are patient enough to spend that much time trying to help someone so thank you

xapproachesinfinity · Answer

yes! need me just tag @x...

anonymous · Answer

ok

xapproachesinfinity · Answer

no problem! i could have just given you the answer but that won't help at all :)

xapproachesinfinity · Answer

good luck :)