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

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



cool cool cool

CPhill  Jul 24, 2018

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