Question

Find DRG of $f(x)=\frac{1 - x + 2\sqrt{-x}}{1 + x}$

Answer 1

$(-∞,-1)\cup(-1,0]$

Answer 2

Domain constraints

1. Under the radical: $-x \ge 0$ ⇒ $x \le 0$.
2. Denominator nonzero: $1 + x \neq 0$ ⇒ $x \neq -1$.

Combining these gives

$$x \le 0,\quad x \neq -1$$

in interval notation:

$$\boxed{(-∞, -1)\cup(-1, 0]}$$