Question

The domain of the function $f(x)=\frac{1}{{\log }_{10}(1-x)}+\sqrt{x+2}$ is

• A. $[-2,0)\cap (0,1)$
• B. $[-2,0)$
• C. $[-2,1)$
• D. $[-2,0)\cup (0,1)$

Answer 1

Answer: (D)

$1-x>0,1-x\ne 1$
$x-1<0x\ne 0x+2\ge 0$
$x<1x\ge -2$
$\therefore x\in [-2,0)\cup (0,1)$