Question

What is the domain and range of `f(x)=sqrt(x^2 +4)`?

Answer 1

`f(x)=sqrt(x^2+4)` is defined for all Real values of `x`
The Domain is `x epsilon RR`
(actually `f(x)` is valid for `x epsilon CC` but I will assume we are not interested in Complex numbers).

If we restrict `x epsilon RR`
then `f(x)` has a minimum value when `x=0` of
`sqrt(0^2+4) = 2`
and the Range of `f(x)` is `[2,+oo)`

(If we allow `x epsilon CC` the Range of `f(x)` becomes all of `CC`)