Question

How do you find the domain of `g(x) = root3(x+3)`?

Answer 1

The domain is `RR`. See explanation.

Explanation:

To find the domain of a function you have to think of all real values of `x` for which the function's value can be calculated.

In the given function there are no excluded values of `x`, therfore the domain is `RR`.

Note that if there was square root sign (instead of cubic root) then the domain would only be the set for which

`x+3 >=0`

because square root (or generally root of an even degree) cannot be calculated for negative values.

Answer 2

Domain of `g(x)=root(3)(x+3)` is `x:x inRR and x in(-oo,oo)`

Explanation:

We have a cube root here, Note that while even powers are all positive, odd powers can be negative as well.

Therefore whether `x+3` is positive or negative, we can find its cube root.

Hence, domain of `g(x)=root(3)(x+3)` is `x:x inRR and x in(-oo,oo)`