What is the domain of the function $$w(x) = \sqrt{x-2} + \sqrt[3]{x-3}~?$$ Express your answer in interval notation.
\(w(x) = \sqrt{x-2} + \sqrt[3]{x-3}~\)
The domain is that which is the most restrictive for both parts of the function
The second term has a domain of all real numbers because we can take the cube root of all real numbers
However.....the frist term is only defined from [2, inf)
So.....this is the domain