# How do you find the domain and range of f(x)= -sqrt(x-3)?

Sep 16, 2015

Domain $\left\{x \in \mathbb{R} , x \ge 3\right\}$
$\left\{y \in \mathbb{R} , y \le 0\right\}$
For a function from real to real x-3 should be $\ge 0$, hence domain is $\left\{x \in \mathbb{R} , x \ge 3\right\}$.
For range solve $y = - \sqrt{x - 3}$ for x, and to note that y would have to be all negative real numbers.
$x = {y}^{2} + 3$, hence $y \le 0$ Range would be $\left\{y \in \mathbb{R} , y \le 0\right\}$