Question

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

Answer 1

Domain: `x>=2`
Range: `y>=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)>=0`

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

`x>=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>=2`, the range will be `y>=0`, because the lowest value we can plug in, `2`, will evaluate to `0`.