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Compute the domain of the real-valued function\(f(x)=\sqrt{3-\sqrt{5-\sqrt{x}}}. \)

 Jul 13, 2021
 #1
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x   must  be  ≥  0

 

And   5 - sqrt x     must  be ≥  0

So

5 - sqrt x  ≥  0

5 ≥  sqrt x        square  both sides

25 ≥  x

 

So.....the  domain  is

 

[ 0 ,  25  ] 

 

See  the graph here  :  https://www.desmos.com/calculator/gxk17ddz6u

 

cool cool cool

 Jul 13, 2021

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