Question

What is the domain and range of `y=sqrt( x-4)`?

Answer 1

Domain: `x>=4`
Range: `y>=0`

Explanation:

Any number inside a square root has to be positive or `0` or else, the answer will be a complex solution. With that being said, `x-4` has to be greater than or equal to `0`:

`x-4>=0`

Solve this equation to find the domain. Add `4` to both sides:

`x>=4`

So our domain is that x has to be greater than or equal to `4`.

Since the square root can never yield a negative number, `y` will always be positive or `0`. So the range of `y` is that:

`y>=0`