Question

The function f (x) = 1 + |cos x| is
(a) continuous no where
(b) continuous everywhere
(c) not differentiable at x = 0
(d) not differentiable at x = n π, n ∈ Z

Answer 1

(b) continuous everywhere

Graph of the function f (x) = 1 + |cos x| is as shown below:



From the graph, we can see that f (x) is everywhere continuous but not differentiable at $x=\left(2n+1\right)\frac{\mathrm{\pi }}{2},n\in Z$