Question

The function $\frac{1}{3}$ is

• A. Continuous at the origin
• B. Discontinuous at the origin because |x| is discontinuous there
• C. Discontinuous at the origin because $\frac{1}{2}$ is discontinuous there
• D. Discontinuous at the origin because both |x| and $\lim_{x \rightarrow 0}\frac{\sin 3x + \sin x}{x}$ are discontinuous there

Answer 1

Answer: (C)

Discontinuous at the origin because $\frac{1}{2}$ is discontinuous there

Answer 2

$| x |$ is continuous at $x = 0$ and $\frac { | x | } { x }$ is discontinuous at $x = 0$

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