Find the domain of function $f(x)=\frac{1}{\sqrt{\{\sin x\}+ \{\sin(π-x)\}}}$, where {.} denotes the fractional part function.
Answer & explanation
Correct answer: option 1
$f(x)=\frac{1}{\sqrt{\{\sin x\}+ \{\sin(π-x)\}}}=\frac{1}{\sqrt{\{\sin x\}+ \{-\sin x\}}}$
Now, $\{\sin x\}+ \{-\sin x\}=\left\{\begin{matrix}0,&\sin x\,is\,an\,integer\\1,&\sin x\,is\,not\,an\,integer\end{matrix}\right.$
For f(x) to get defined,
$\{\sin x\} + \{-\sin x\} ≠0$
or $\sin x$ ≠ integer
or $\sin x ≠±1, 0$
or $x≠\frac{nπ}{2},\,n∈I$