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
(c) $|x|$ is continuous at $x = 0$ and $\frac{{|x|}}{x}$ is also discontinuous at $x = 0$

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

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