This is the question from my text book:

Show that f:R-{3}—>R defined by f(x)=(x-2)/(x-3) is not onto. This is what I have done so far:

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

[tex]\Rightarrow[/tex] x=(3y-2)/(y-1)

For y=1, x is undefined.

This means for y=1 there is no pre-image x in the Domain. Hence, the function is not onto.

I doubt that the function is not onto just because for y=1, x is undefined. What have I done wrong and how do I prove that the function is not onto?