The function f(x) = 1 + |sin x| is

continuous nowhere continuous everywhere discontinuous at x = 0 None of these

continuous everywhere

$f(x) = 1 + |\sin x|$ so for $\sin x ≥ 0 ⇒ f (x) = 1 + \sin x$ $\sin x ≤ 0 ⇒ f(x) = 1 − \sin x$ for $\underset{x→0^+}{\lim}f(x)=1$ $\underset{x→0^-}{\lim}f(x)=1$ so f(x) is continuous for all $x∈R$