Question

The domain of $f\left(x\right)=\sqrt{\cos x-1}$ is

• A. $R-\{n\pi :n\in Z\}$
• B. $\{n\pi :n\in Z\}$
• C. $\{2n\pi :n\in Z\}$
• D. $(-\infty ,\infty )$

Answer 1

The correct option is C $\{2n\pi :n\in Z\}$

For $f$ to be defined term under square root has to be greater than zero.
$\Rightarrow \cos x-1\ge 0$
$\Rightarrow \cos x\ge 1$
Only possible if $\cos x=1$
$\Rightarrow x=2n\pi \forall n\in Z$