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# Domain

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Compute the domain of the real-valued function $f(x) = \sqrt{1 + \sqrt{2 - \sqrt{x}}}$.

Apr 7, 2022

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Domain:  0  <=  x  <=  4

The outermost  sqrt( 1 + ... ) has no effect upon the domain.

The  sqrt( 2 - sqrt(x) )  requires that x can be no larger than 4.

The  sqrt(x)  requres that x can be no smaller than 0.

Apr 7, 2022