Question

Examine the continuity of the following function :

\(f(x) = \begin{cases} \frac{x}{2|x|}&,& \quad x≠0 \\ \frac{1}{2}&, & \quad x=0 \end{cases}\) at x = 0

Answer 1

Given,

\(f(x) = \begin{cases} \frac{x}{2|x|}&,& \quad x≠0 \\ \frac{1}{2}&, & \quad x=0 \end{cases}\) 

For continuity at x = 0, we have

f(0) = \(\frac{1}{2}\)

Hence, LHL ≠ RHL

So, f(x) is discontinuous at x = 0.