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

4 x + 9

- 36 - (1.2 x + 5)^{2} + 3

f (x) = \frac{9 + x}{1 - 9 x}

f (x) = \frac{x}{e ^{x^{2} \cdot 5 x + 6}} + ln (x - 1)

\frac{( x + 2 ) ( x - 3 )}{x ^{2} - 4}

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