Question

Find all points of discontinuity of f, where f is defined as follows :

\(f(x)=\begin{cases} |x|+3, & \quad x≤ -3\\ -2x , & -3<x<3\\ 6x+2, & \quad x≥3 \end{cases}\)

Answer 1

We have,  \(f(x)=\begin{cases} |x|+3, & \quad x≤ -3\\ -2x , & -3<x<3\\ 6x+2, & \quad x≥3 \end{cases}\)

Clearly, the possible points of discontinuity of f are 3 and –3. 

[∵ For all other points f(x) is a linear polynomial, which is continuous everywhere]

So, the only point of discontinuity of f is x = 3.