Question

$f(x=)\frac{\left|x\right|}{x},0\ne f\left(0\right)=1$ $f\left(x\right)$ at $x=0$ is

• A. Left continuous
• B. Right continuous
• C. Not determined
• D. Continuous

Answer 1

Answer: (B)

Right continuous

$f\left(x\right)=\frac{\left|x\right|}{x}\therefore f\left(x\right)=\frac{x}{x}x>0=1x>0andf\left(x\right)=-\frac{x}{x}x<0=-1x<0andf\left(x\right)=1x=0=1x=0$

${lim}_{x\to 0-}f\left(x\right)=-1{lim}_{x\to 0+}f\left(x\right)=1f(x=0)=1$

Therefore, the function is right continuous.