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# domain

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Find the domain of the function f(x) = sqrt(sqrt(x^2 - 16) + 3).

May 3, 2022

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If there is a square root, the expression inside must be nonnegative.

As a result, $$x^2 - 16 \geq 0$$. You can solve this to get the domain of f(x).

Remarks: You do not need to consider $$\sqrt{x^2 - 16} + 3 \geq 0$$ because $$\sqrt{x^2 - 16} + 3 \geq 0 + 3 = 3 > 0$$ if sqrt(x^2 - 16) is defined.

May 3, 2022