Question

If $f\left(x\right)=\mathrm{sgn}(2\sin x+a)$ is continuous for all $x$ then possible values of "$a$"

• A. $a\in R$
• B. $a=2$
• C. $a<-2\text{or}a>2$
• D. $-2<a<2$

Answer 1

The correct option is C $a<-2\text{or}a>2$

$-1\le \sin x\le 1$

$a-2\le 2\sin x+a\le a+2$

For $f\left(x\right)=sgn(2\sin x+a)$to be continuous,

either $a-2>0⟹a>2$

or, $a<-2$

So, $aϵ(-\infty ,-2)\cup (2,\infty )$