Compute the domain of the real-valued function f(x) = sqrt(3 - sqrt(8 - sqrt(x))).
+130020 \( sqrt(3 - sqrt(8 - sqrt(x)))\)
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
