# What is the domain and range of g(x) = sqrt(x-2)?

Mar 10, 2018

Domain: $x \setminus \ge 2$
Range: $y \ge 0$

#### Explanation:

If we're concerned with real solutions, $\sqrt{x - 2}$ cannot take on any values less than zero. We can model this with the following inequality to figure out the domain:

$\sqrt{x - 2} \setminus \ge 0$

Squaring and adding $2$ to both sides, we get:

$x \setminus \ge 2$

(This is our domain)

What else do we know about square roots? Above, we said we cannot have any values less than zero. This is our range.

Given a domain of $x \ge 2$, the range will be $y \ge 0$, because the lowest value we can plug in, $2$, will evaluate to $0$.