Question

Can someone please explain ? I was thinking (d) but I'm not sure !
Why is the following function discontinuous at x=1 ?
f(x)= 1/(x-1) x cannot = 0
2 x=1
answer choices.....
(a) f(1) does not exist
(b) lim f(x) does not exist (or is infinite)
x->1
(c) Both (a) & (b)
(d) f(1) and lim f(x) exist, but they are not equal.
x-> 1

Answer 1

Well, we know that f(1) does exist, since when x is 1 the function f(1) is 2.
So a and c are eliminated, and since c also includes b that's also not an answer...
but that's just the lazy way to solve this.

Answer 2

You could check to see whether or not b is an answer by finding the limit(s) as x approaches 1.

Answer 3

I guess I'm also having trouble finding the limits would I just plug in 1 for the first function ?

Answer 4

Oo, I misread the question. It's over x-1 not x+1. Don't trust my answer, let me skim through again.

Answer 5

Okay

Answer 6

Okay, so the function has an asymptote when x=1, unless your restriction was supposed to be x cannot be 1?

Answer 7

If that isn't an error then actually (c) is correct. I can explain after clarification. The restriction would change the ans.

Answer 8

at 1/(x-1) I'm told x cannot equal 1 and that at 2 x=1

Answer 9

Okay, so then if you struggle to work out limits algebraically, this one can be graphed.