Question

Domain of $f\left(x\right)=\sin \left(\ln \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right)$ is

• A. $(-2,2)$
• B. $(-2,1)$
• C. $(1,2)$
• D. $(-1,1)$

Answer 1

The correct option is B $(-2,1)$

$f\left(x\right)=\sin \left(\ln \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right)$
$\frac{\sqrt{4-x^2}}{1-x}>0$ & $1-x\ne 0$
$\Rightarrow x\ne 1$
$\therefore 4-x^2>0$
&$1-x>0$
$x<1$
Combining the domains, we have
$x\in (-2,1)$