Question

Find all points of discontinuity of f, where f is defined as follows. f(x) = {|x| + 3, x ≤ -3 and -2x, -3 < x < 3 and 6x + 2, x ≥ 3}

Answer 1

Given, function is

Firstly we verify continuity at x = - 3 and then at x = 3. Continuity at x = -3

.'. f(x) is continuous at x = -3. So, x = - 3 is the point of continuity.

f is discontinuous at x = 3.

Now, as f(x) is a polynomial function for x < - 3, - 3 < x < 3 and x > 3, so it is continuous in these intervals.

Hence, only x = 3 is the point of discontinuity of f(x).