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

2 Answers
Jun 23, 2017

Answer:

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.

Jun 23, 2017

Answer:

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)#