The function f(x)=|x|+|x| x is - Vidyadip

MCQ

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

A
Continuous at the origin
B
Discontinuous at the origin because $|x|$ is discontinuous there
✓
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

Correct option: C.

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

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

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