Explain why the solution f(x)=2 is undefined.

[gtal3x]

Hello there, just got stack at the question "Explain why the solution f(x)=2 is undefined." where f(x)= 2x/x-1. I used to know why is undefined, but forgot. Maybe because if x=1 than that I can't multiply the both sides by x-1, or something like that?

EDIT
I thought to post a complete question as I realize that I have more problems.

The function f(x) is defined as: f(x)= 2x/x-1
(i) Evaluate f(2) <<< Easy
(ii) Evaluate f(-2) <<< same...
(iii) Explain why the solution f(x)=2 is undefined. <<< SOLVED
(iv) For 2<x<=5 state the range of function <<< Here as well, dont understand what to do...
(v) Sketch the curve of y = f(x) showing all intercepts and asymptotes <<< Well i have the sketch in front of me, there is an asymptote at x=1, I understand that, because when x=1-1 x=0 and 2 can not be devided by 0, but there is an asyptode at y=1 as well, now I dont understand why is there an asymptote.

Many thanks

 

[Loren]

First, I think you mean 2x/(x-1)

If f(x)=2, then 2x/(x-1) = 2 and x=???

 

[gtal3x]

First, I think you mean 2x/(x-1)

If f(x)=2, then 2x/(x-1) = 2 and x=???

Oh yeah I think i got it. Multiply both sides by (x-1) we get 2x=2x-2, take the 2x to the other side we get 0=-2, which of course can not be true, so the solution is undefined...

Thanks for this one