Let $f: \mathbb{R} ightarrow \mathbb{R}$ be defined by $f(x)=\frac{|x|}{x}, x
eq 0$. Then

Question

Let $f: \mathbb{R} ightarrow \mathbb{R}$ be defined by $f(x)=\frac{|x|}{x}, x 
eq 0$. Then

Professor PC Thomas Classes · Answer

The signum function $f(x) = \frac{|x|}{x}$ is continuous everywhere except at $x=0$. Thus it's continuous in $(0,\infty)$ or similar open intervals avoiding 0.