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

 Jul 24, 2018
 #1
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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

 Jul 24, 2018

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