What is the domain of the function \(w(x) = \sqrt{x-2} + \sqrt[3]{x-3}~?\) Express your answer in interval notation.

Lightning Jul 24, 2018

#1**+1 **

We have no restriction on the domain for the second function because we can take the cube root of any real number

However....for the first function, x cannot be < 2 because we would have a negative square root which does not produce a real value

So......we must take the most restrictive domain for both functions....this is [ 2, infinity )

Here's a graph : https://www.desmos.com/calculator/ant19juary

CPhill Jul 24, 2018