# f(x)=1/x continuous?

• Jul 6th 2012, 11:20 AM
Jzon758
f(x)=1/x continuous?
Is f(x)=1/x considered continuous? A practice test I was doing said it was, but I figured it would have to be discontinuous at x=0. Does it possibly have to do with 0 not being in the domain? The simple definition of continuity given to me was if the graph could be drawn without picking up your pencil; this is why I do not see how 1/x can be continuous.
• Jul 6th 2012, 11:58 AM
Plato
Re: f(x)=1/x continuous?
Quote:

Originally Posted by Jzon758
Is f(x)=1/x considered continuous? A practice test I was doing said it was, but I figured it would have to be discontinuous at x=0. Does it possibly have to do with 0 not being in the domain? The simple definition of continuity given to me was if the graph could be drawn without picking up your pencil; this is why I do not see how 1/x can be continuous.

On what set? Not on $\displaystyle \mathbb{R}$. It is continuous on $\displaystyle (-\infty,0)\cup (0,\infty)$
• Jul 6th 2012, 12:00 PM
skeeter
Re: f(x)=1/x continuous?
$\displaystyle f(x) = \frac{1}{x}$ is continuous over its domain.
• Jul 6th 2012, 10:47 PM
Jzon758
Re: f(x)=1/x continuous?
Okay good. I thought I was missing out on something regarding the definition of continuity. I think the practice test must be flawed. Thanks!