If f(x)=sgn(sin x+a) is continuous for all x, then possible values of a are given by

Question

If f(x)=sgn(sin x+a) is continuous for all x, then possible values of a are given by (A) |a| ≤ 1 (B) |a|< 1 (C) |a| > 1 (D) |a| ≥ 1

Tardigrade Admin · Accepted Answer

f(x)=sgn(sin x+a) is continuous for all x if sin x+a ≠ 0 ⇒ -sin x ≠ a ⇒ a< -1 or a> 1 ⇒ |a| > 1

Q. If $f (x) = s g n (s in x + a)$ is continuous for all $x$ , then possible values of $a$ are given by