Question

How do you find the domain and range for `g(x)=sqrt( x-1)`?

Answer 1

The domain is `x in [1, +oo)`. The range is `g(x) in [0, +oo)`

Explanation:

What's under the `sqrt` sign is `>=0`

Therefore,

`x-1>=0`

`x>=1`

The domain is

`x in [1, +oo)`

When `x=1`, `=>`, `y=0`

And

`lim_(x->+oo)g(x)=lim_(x->+oo)sqrt(x-1)=+oo`

The range is `g(x) in [0, +oo)`

graph{sqrt(x-1) [-10, 10, -5, 5]}