The domain of f x = sinlog 4 - x 2 1 - x is

We have,

$f\left(x\right)=\mathrm{sinlog}\left(\frac{\sqrt{4-x^2}}{1-x}\right)$

Domain of $\sin \left(\theta \right)$ is $R$.

${\log }_a\left(x\right)$ is defined for $x,a>0$ and $a\ne 1$.

For $f\left(x\right)$ to be defined,

$\frac{\sqrt{4-x^2}}{1-x}>0$ and $x\ne 1$

$\Rightarrow \frac{1}{1-x}>0$

Since, $\sqrt{4-x^2}\ge 0 \forall x\in R$

$\Rightarrow \frac{1}{1-x}>0$

$\Rightarrow x\in \left(-\infty ,1\right)$

And, $\left(-2,1\right)\subset \left(-\infty ,1\right)$.