1. Tardigrade
  2. Question
  3. Mathematics
  4. If f(x)=sgn(sin x+a) is continuous for all x, then possible values of a are given by

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Continuity and Differentiability

Solution:

$f(x)=sgn(sin x+a)$ is continuous for all $x$ if $\sin x+a \neq 0$
$\Rightarrow -sin x \neq a$
$ \Rightarrow a<\,-1$
or $a>\,1 $
$\Rightarrow |a| >\,1$