Question

Let f(x) = 1 + x, 0 ≤ x ≤ 2

f(x) = 3 - x, 2 < x ≤ 3

Determine the form of g(x) = f [f(x)] and hence find the points of discontinuity of g, if any

Answer 1

Now, RHL (at x = 2) = 2 and LHL (at x = 2) = 0 Also, RHL (at x = 1) = 1 and LHL (at x = 1) = 3

Therefore, f(x) is discontinuous at x =1, 2

.'.  f[f (x)] is discontinuous at x = {1, 2}.