Question

The function $f(x)=|x|+\frac{|x|}{x}$ is

(A) Continuous at the origin

(B) Discontinuous at the origin because $|x|$ is discontinuous there

(C) Discontinuous at the origin because $\frac{|x|}{x}$ is discontinuous there

(D) Discontinuous at the origin because both $|x|$ and $\frac{|x|}{x}$ are discontinuous there

Answer 1

Since, $|x|$ is discontinuous at $x=0$ and $\frac{|x|}{x}$ is also discontinuous at $x=0$

$\therefore f(x)=|x|+\frac{|x|}{x}$ is discontinuous at $x=0$

So, The correct option will be (D).