What is the domain of f(x)=sqrt(1-\sqrt{4-x^2)} ?

The domain of f(x)=sqrt(1-\sqrt{4-x^2)} is -2<= x<=-sqrt(3)\lor sqrt(3)<= x<= 2

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domain of f(x)=sqrt(1-\sqrt{4-x^2)}

domain

f (x) = 1 - 4 - x^{2}

- 2 \leq x \leq - 3 or 3 \leq x \leq 2

Interval Notation

[- 2, - 3] \cup [3, 2]

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq - 3 or 3 \leq x \leq 2

The function domain

- 2 \leq x \leq - 3 or 3 \leq x \leq 2

What is the domain of f(x)=sqrt(1-\sqrt{4-x^2)} ?
The domain of f(x)=sqrt(1-\sqrt{4-x^2)} is -2<= x<=-sqrt(3)\lor sqrt(3)<= x<= 2