# Homework Help: Subset math help

1. Aug 21, 2010

### annoymage

1. The problem statement, all variables and given/known data

F : R-{1/3} ---> R-{0}
F(x) = 1/(3x-1)

to show R-{0} $$\subseteq$$ image of F

for any y in R-{0}, if we try to solve y=1/(3x-1), we find x=(1+y)/3y,

F((1+y)/3y)=y

2. Relevant equations

R is real number

3. The attempt at a solution

so, if (1+y)/3y are the values for x in R-{0} such that F((1+y)/3y)=y

but i don't understand, how is that showing R-{0} $$\subseteq$$ image of F

2. Aug 21, 2010

Re: subset

You have shown that if y is in R\{0}, then it is in the image of F, too, since for such a number y there exists a number x = (1 + y) / 3y whose image under F is y. (btw the image of F is defined as {F(x) : x is in R\{1/3}})

3. Aug 21, 2010

### annoymage

Re: subset

thanks, i get it now ^^