What is the domain of f(x)=sqrt(4-\sqrt{24-2x-x^2)} ?

The domain of f(x)=sqrt(4-\sqrt{24-2x-x^2)} is -6<= x<=-4\lor 2<= x<= 4

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domain of f(x)=sqrt(4-\sqrt{24-2x-x^2)}

domain

f (x) = 4 - 24 - 2 x - x^{2}

- 6 \leq x \leq - 4 or 2 \leq x \leq 4

Interval Notation

[- 6, - 4] \cup [2, 4]

Solution steps

Find non-negative values for radicals:

- 6 \leq x \leq - 4 or 2 \leq x \leq 4

The function domain

- 6 \leq x \leq - 4 or 2 \leq x \leq 4

2 - 4 x

f (x) = \frac{x + 2}{x ^{2} + 4}

f (x) = \frac{1}{2 x + 7}

\frac{x - 4}{x ^{2} - 2 x - 15}

f (x) = \frac{x - 4}{x}

What is the domain of f(x)=sqrt(4-\sqrt{24-2x-x^2)} ?
The domain of f(x)=sqrt(4-\sqrt{24-2x-x^2)} is -6<= x<=-4\lor 2<= x<= 4