Proving that a function is not Onto

Proving that a function is not Onto

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)
$$\Rightarrow$$ 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?
UserKunal123

Posts: 1
Joined: Tue Jul 09, 2019 2:58 pm
Reputation: 0

Re: Proving that a function is not Onto

The only thing you have "done wrong" is doubt your proof! Yes, there is NO value of x such that f(x)= 1. That violates the definition of "onto". Why do you doubt it?
Guest