Browse Questions

Find the domain of $sin(log(\large\frac{\sqrt{4-x^2}}{1-x}))$

(A) $(-1,1)$

(B) $(-2,1)$

(C) $(0,1)$

(D) $(-1,0)$

$f(x)=sin(log(\large\frac{\sqrt{4-x^2}}{1-x}))$
$\Rightarrow\:\large\frac{\sqrt{4-x^2}}{1-x}>0$
$\Rightarrow\:4-x^2>0\:\:and\:\:1-x>0$
$\Rightarrow\:x^2<4\:\:and\:\:x<1$
$\Rightarrow\:|x|<2\:\:and\:\:x>1$
$\Rightarrow\:x\in (-2,1)$
Domain $=(-2,1)$