Question

Discuss the continuity of the function f(x) = | x | + | x - 1 | in interval [-1, 2].

Answer 1

i. Let g(x) = |x|.

Then, g(x) = x, for all x ≥ 0

= -x, for all x < 0

Now, g(0) = 0

Let x ∈ [-1, 2] - {1}. Since h(x) is a polynomial in [–1, 1) and (1, 2], it is continuous in these intervals.

∴ h(x) = |x – 1| is continuous in [– 1, 2].

Now, f(x) = g(x) + h(x) and g(x) as well as h(x) are continuous on [–1, 2].

The sum of two continuous functions is a continuous function.

Hence, f(x) is continuous in [– 1, 2].