Find the domain following function given by: f(x)=1 1- - Vidyadip

Question

Find the domain following function given by:
$\text{f(x)}=\frac{1}{\sqrt{1-\cos\text{x}}}$

✓

Answer

We have, $\text{f(x)}=\frac{1}{\sqrt{1-\cos\text{x}}}$
Now $-1\leq\cos\text{x}\leq1$
$\Rightarrow-1\leq-\cos\text{x}\leq1$
$\Rightarrow0\leq-\cos\text{x}\leq1$
$1-\cos\text{x}\neq0$
So, f(x) is defined, if $1-\cos\text{x}\neq0$
$\therefore \cos\text{x}\neq1$
$\therefore\text{x}\neq2\text{n}\pi, \text{n}\in\text{Z}$
$\therefore$ Domain of f is R $\big\{2\text{n}\pi: \text{n}\in\text{Z}\big\}$

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