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Compute the domain of the real-valued function f(x) = sqrt(3 - sqrt(8 - sqrt(x))).

 Feb 14, 2022
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\( sqrt(3 - sqrt(8 - sqrt(x)))\)

 

 

The least   value in  the domain  will  be  when x = 0

 

So we have  

 

sqrt ( 3 - sqrt ( 8 - sqrt ( 0 ) ) )  =  sqrt ( 3 - sqrt 8 ) =  sqrt ( 3 - 2sqrt 2)

 

Since we cannot take the square root of a negative, the greatest value in the domain = 64  because

 

sqrt ( 3 - sqrt ( 8 - sqrt (64)) )  =  sqrt ( 3 - sqrt ( 8  - 8) ) = sqrt ( 3 - 0 ) =  sqrt 3

 

See the graph here : https://www.desmos.com/calculator/0nd567etzs

 

 

cool cool cool

 Feb 14, 2022

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