Determine the intervals on which the function is continuous. f(x) (5-x, x2)

Question

Determine the intervals on which the function is continuous.

f(x) (5-x, x<=2) and (2x-3, x>2)

anonymous · Answer

would it just be all real numbers? or all besides x=2 since the graphs don't touch at 2?

anonymous · Answer

$5-x$ and $2x-3$ are continuous for their respective pieces, but you have to check if $\displaystyle\lim_{x\to2}f(x)$ exists. To do that, you have to check the one-sided limits, since the function takes on $5-x$ for values less than 2 and $2x-3$ takes on values greater than 2.

anonymous · Answer

Basically, if $\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2^+}f(x)$, then $f(x)$ is continuous. If they're not equal, $f(x)$ is not continuous at 2.

anonymous · Answer

I see. So in this case the lmiits of the functions would be 3, and 1 respectively. Since they're not equal, not continuous at 2? Just checking.

anonymous · Answer

Yes, that's right.

anonymous · Answer

Thanks!

anonymous · Answer

You're welcome!