Find the domain of function f(x)= sin(log_e((√(4-x^2))/(1-x)))

We have $f(x)= \sin(\log_e(\frac{\sqrt{4-x^2}}{1-x}))$

We must have $4-x^2> 0$ and $1-x>0$

$⇒x^2<4$ and $x<1$

$⇒-2 < x <2$ and $x<1$

$⇒-2 < x < 1$

Thus, domain of f(x) is (-2, 1)