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

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

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domain of f(x)=sqrt((1-x^2)/(x^2-4))

domain

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

- 2 < x \leq - 1 or 1 \leq x < 2

Interval Notation

(- 2, - 1] \cup [1, 2)

Solution steps

Find non-negative values for radicals:

- 2 < x \leq - 1 or 1 \leq x < 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

- 2 < x \leq - 1 or 1 \leq x < 2

f (x) = \frac{x ^{2} + 9 x + 20}{2 x + 8}

(- 22, - 15), (11, 14)

6 x - 2 y = - 2

y = 4 x + 7

f (x) = \frac{x ^{2} - 3 x - 10}{x + 6}

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