Homework Help: I've gone full retard stupid continuity question

1. Sep 23, 2010

charity4thep

is the equation f(x)=(x^2-1)/(x+1) continuous?

i know it can be reduced to f(x)=(x-1) but i remember that in doing so you divide by zero for x=-1 and thus it will be discontinuous at that point...

i dunno i'm really tired tonight

2. Sep 23, 2010

novop

Never go full retard...

The equation is discontinuous when the denominator is zero.

3. Sep 23, 2010

charity4thep

thanks man. been a while since i had calc 1 i don't remember the exact rule of this situation. doesn't help that my high school calc teacher taught me a complete 180 from what my university professor did...

4. Sep 24, 2010

losiu99

Definition of continuity requires a function to be defined in point in which it is continuous.

Last edited: Sep 24, 2010
5. Sep 24, 2010

HallsofIvy

by the way, the problem is not to determine if the "equation" is continuous- it is to determine if the function defined by that equation is continuous. "continuity" is defined for functions, not equations.

The definition of "f(x) is continuous at x= a" has three parts:
1) That f(a) exist.
2) That $\displaytype \lim_{x\to a} f(x)$ exist.
3) That $\displaytype \lim_{x\to a} f(x)= f(a)$.

As losiu99 says, $(x^2- 1)/(x- 1)$ is not defined at x= 1 and so is not continuous there. $(x^2- 1)/(x-1)= x+ 1$ for x not equal to 1 and is not defined at x= 1. Its graph is NOT the straight line y= x+ 1, it is the straight line y= x+ 1 with a hole at (1, 2).-