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

Jun 23, 2017

The domain is $\mathbb{R}$. 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 $\mathbb{R}$.

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

$x + 3 \ge 0$

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

Jun 23, 2017

Domain of $g \left(x\right) = \sqrt[3]{x + 3}$ is $x : x \in \mathbb{R} \mathmr{and} x \in \left(- \infty , \infty\right)$

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 $g \left(x\right) = \sqrt[3]{x + 3}$ is $x : x \in \mathbb{R} \mathmr{and} x \in \left(- \infty , \infty\right)$