Continuity of a function $f(x)=\begin{cases} -1, & x<0 \\ b, & x=0 \\ +1, & x>0 \end{cases}$

Question

This is a homework problem so I would prefer hints to answers.

$b \in \mathbb{R} $

$f(x)=\begin{cases} -1, & x<0 \\ b, & x=0 \\ +1, & x>0 \end{cases}$

Does a number b exist so that $f(x)$ is continous?

I believe $f(x)$to be continuous for $x>0$ and $x<0$ due to the fact that if i made the function $g(x)= 1 $ $\forall x > 0$ it would be continous, same for -1. but I'm not sure how to go about it for $x=0$

Answer 1

Hint:

• You should be able to conclude from observing $\lim_{x \to 0^+} f(x)$ and $\lim_{x \to 0^-} f(x)$