Question

If f(x) = sin log $\left(\frac{\sqrt{4-x^2}}{1-x}\right)$, then the domain of f(x) is ___

• A. $(1,2)$
• B. $(-2,1)$
• C. $(-1,2)$
• D. $(0,2)$

Answer 1

The correct option is B

$(-2,1)$

Given, f(x) = sin log$\left(\frac{\sqrt{4-x^2}}{1-x}\right)$
For domain, $\frac{\sqrt{4-x^2}}{1-x}>0,and1-x\ne 0\Rightarrow (1-x)>0and4-x^2>0\Rightarrow x<1and|x|<2\Rightarrow -2<x<1$
Thus, domain $ϵ$ (-2, 1)