Question

Let f(x) = |x – 2| – 1, 0 ≤ x ≤ 4 and g(x) = 2 – |x|, –1 ≤ x ≤ 3 Then discuss the continuity of the function (fog)(x).

Answer 1

We have

Now (f0g)(x)

= f(g(x))

Thus, f(x) is continuous in [– 1, 2].