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

The domain of f(x)=sqrt(1-2\sqrt{3-2x-x^2)} is -3<= x<=-(sqrt(15))/2-1\lor (sqrt(15))/2-1<= x<= 1

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domain of f(x)=sqrt(1-2\sqrt{3-2x-x^2)}

domain

f (x) = 1 - 2 3 - 2 x - x^{2}

- 3 \leq x \leq - \frac{15}{2} - 1 or \frac{15}{2} - 1 \leq x \leq 1

Interval Notation

[- 3, - \frac{15}{2} - 1] \cup [\frac{15}{2} - 1, 1]

Solution steps

Find non-negative values for radicals:

- 3 \leq x \leq - \frac{15}{2} - 1 or \frac{15}{2} - 1 \leq x \leq 1

The function domain

- 3 \leq x \leq - \frac{15}{2} - 1 or \frac{15}{2} - 1 \leq x \leq 1

What is the domain of f(x)=sqrt(1-2\sqrt{3-2x-x^2)} ?
The domain of f(x)=sqrt(1-2\sqrt{3-2x-x^2)} is -3<= x<=-(sqrt(15))/2-1\lor (sqrt(15))/2-1<= x<= 1