Algebra problem help

[coder1]

Ok, I know this is somewhat elementary, but I am trying to resolve this problem below and for the life of me I can not find any references in my book or online to this problem.

Given f(x)=x/(3x+2) find f^-1(x)


Is this an inverse function?

what is throwing me off is that -1

 

[TuxDave]

yes.. it's the inverse function. You need to find a function such that:

if f(x)=y then f^-1(y)=x

 

[Goosemaster]

yes....



f(x) =y

such as f(x)=5x is the same as y=5x for your purposes

1. find what x=
2. once you get x = blah, replace the x's with y's and the y's with x's

 

[coder1]

so solving for x I get x=-2y/3y

Do I just switch X and Y?

Would the answer be f^-1(x)=-2x/3x

 

[TuxDave]

Originally posted by: coder1
so solving for x I get x=-2y/3y

Do I just switch X and Y?

Would the answer be f^-1(x)=-2x/3x

uhh... double check your work. There's no way x=-2y/3y

 

[Goosemaster]

grpah it and check


ex. Here's your original function: y=3x-2
Try to solve for "x =":

y+2 = 3x

x= (y+2)/3


Switch x and y; "y =" is the inverse.

y=(x+2)/3

 

[coder1]

LOL, thats what I get for trying to figure this stuff out at 11:00pm. Thanks so much for everyones help! I now think I somewhat understand it.

 

[cronos]

Originally posted by: coder1
Ok, I know this is somewhat elementary, but I am trying to resolve this problem below and for the life of me I can not find any references in my book or online to this problem.

Given f(x)=x/(3x+2) find f^-1(x)

Is this an inverse function?

what is throwing me off is that -1

yes. inverse function. the -1 is actually the inverse.

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

so the inverse function is:

f^-1(x) = 2x/(1-3x)