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Find the domain of the function $$f(x)=\sqrt{3+5-\sqrt{x}}.$$

1 Answer

2 votes

The stuff under the first or outermost square root needs to be nonnegative.


3+5-√(x) \ge 0\\\\8-√(x) \ge 0\\\\8 \ge √(x)\\\\√(x) \le 8\\\\x \le 8^2\\\\x \le 64\\\\

Also, we need to have
x \ge 0 aka
0 \le x so the stuff under the second square root is also nonnegative.

Glue together
0 \le x \ \text{ and } \ x \le 64 to end up with
0 \le x \le 64 as the domain.

User George Baker
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