1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Sep 23, 2010 #1
    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. jcsd
  3. Sep 23, 2010 #2
    Never go full retard...

    The equation is discontinuous when the denominator is zero.
  4. Sep 23, 2010 #3
    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...
  5. Sep 24, 2010 #4
    Definition of continuity requires a function to be defined in point in which it is continuous.
    Last edited: Sep 24, 2010
  6. Sep 24, 2010 #5


    User Avatar
    Science Advisor

    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 [itex]\displaytype \lim_{x\to a} f(x)[/itex] exist.
    3) That [itex]\displaytype \lim_{x\to a} f(x)= f(a)[/itex].

    As losiu99 says, [itex](x^2- 1)/(x- 1)[/itex] is not defined at x= 1 and so is not continuous there. [itex](x^2- 1)/(x-1)= x+ 1[/itex] 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).-
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook