Question

Discuss the continuity and differentiability of the function,
$f\left(x\right)=\left[\begin{array}{cc}\frac{x}{1+|x|}& |x|>1\\ \frac{x}{1-|x|}& |x|\le 1\end{array}\right]$

Answer 1

$\underset{x\to 1^{-}}{lim}f\left(x\right)=\frac{1}{1+1}=\frac{1}{2}$

$\underset{x\to 1^{+}}{lim}f\left(x\right)=\frac{1}{1-1}$ = Doeiut exit

Not continues 1 Not differeatiable