Find the domain of function $f(x)= \sin(\log_e(\frac{\sqrt{4-x^2}}{1-x}))$

(-2, 1) (-2, -1) (2, 1) (2, -1)

(-2, 1)

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)