√(x - 3 ) + 2 find domain and range

Question

`√(x - 3 ) + 2`
find domain and range

Answer 1

Since Domain are all the inputs possible, and square root cannot do negative numbers, x can't go below 3, otherwise the thing will be a complex number. So, your domain is:

`x \geq 3`

Then, your range has to be greater than 0 because a principal square root symbol, if passed a positive number will return a positive answer. So, your range should be:

`x \geq 0`

But, then you add 2 to it, so it then turns into:

`x \geq 2`