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

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Answer 1 · 2017-06-23T08:28:11

The domain is $RR$ . See 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 · 2017-06-23T08:31:30

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

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 $x:x inRR and x in(-oo,oo)$

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