Question

How do you find the domain and range of `f(x) = (x - 3)^(1/2)`?

Answer 1

`(x-3)^(1/2)` is the same as `sqrt(x-3)`

Explanation:

For square roots the argument must be non-negative, or:
`x-3>=0->x>=3`. There is no upper limit.
So the domain is `3<=x< oo`

When `x=3->f(x)=0`, in other words `f(x)>=0`
Also here there is no upper limit as `x` gets larger.
So the range is `0<=f(x)< oo`
graph{sqrt(x-3) [-6.56, 25.48, -4.6, 11.43]}