Question

Find all points of discontinuity of f, where f is defined by f(x) = \(\begin{cases} 2x + 3, & if \;x \leq 2\\ 2x - 3, &if \; x > 2 \end{cases}\)

Answer 1

since LHL ≠ RHL 

limit does not exist and is discontinuous at x = 2 

The function is continuous every where except x = 2 

∴ x = 2 is the point of discontinuity.