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Find the domain of the function $f(x) = \frac{\sqrt{x-2}}{\sqrt{5}} + \sqrt{(x - 1)(x + 2)(x + 4)}.$

 Aug 27, 2023
 #1
avatar+126978 
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Not as hard as it appears

 

The domain is defined  by the  first  function

 

Since we can't have a negative under the first radical , x  must be ≥ 2

 

But notice in the second radical that if x ≥ 2  that this will always result in a positive quantity under this radical

 

So....the domain is  [ 2, inf )

 

cool cool cool

 Aug 27, 2023

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