# Math Help - Discontinuity Point Hole

1. ## Discontinuity Point Hole

Hey, I have a limit discontinuity problem here, and I think I've done it right, but I wanted to make sure that my reasoning was correct.

Question;

For $f(x)=\left\{\begin{array}{cc}\sqrt{x-4},&\mbox{ if }
x>4\\8-2x, & \mbox{ if } x<4\end{array}\right.$
, Use the mathematical definition of continuity to determine whether $f(x)$ is continuous at $x=4$.

I found the left and right hand limits to both equal 0, but the limit cannot be defined directly as x approaches 4, and the function is not defined at 4, so I think there is a point hole in the function at 4. Am I right?

2. Originally Posted by superduper
Hey, I have a limit discontinuity problem here, and I think I've done it right, but I wanted to make sure that my reasoning was correct.

Question;

For $f(x)=\left\{\begin{array}{cc}\sqrt{x-4},&\mbox{ if }
x>4\\8-2x, & \mbox{ if } x<4\end{array}\right.$
, Use the mathematical definition of continuity to determine whether $f(x)$ is continuous at $x=4$.

I found the left and right hand limits to both equal 0, but the limit cannot be defined directly as x approaches 4, and the function is not defined at 4, so I think there is a point hole in the function at 4. Am I right?