# How do you find domain for y = sqrt((4+x) / (1-x) ) ?

Sep 27, 2015

Domain $\left\{x : \mathbb{R} , - 4 \le x < 1\right\}$

Range $\left\{y : \mathbb{R} , y \ge 0\right]$

#### Explanation:

For real y, $4 + x \ge 0 , x \ge - 4$; and $1 - x > 0 , \mathmr{and} , x < 1$

The domain is therefore $\left\{x : \mathbb{R} , - 4 \le x < 1\right\}$

For range, at x=-4, y is 0 and as x increases from -4, y remains positive and as x approaches 1, $y \to + \infty$. Hence Range would be

$\left\{y : \mathbb{R} , y \ge 0\right\}$